Publications by year
In Press
Williams AJ, Menneer T, Sidana M, Walker T, Maguire K, Mueller M, Paterson C, Leyshon M, Leyshon C, Seymour E, et al (In Press). Fostering Engagement with Health and Housing Innovation: Development of Participant Personas in a Social Housing Cohort (Preprint).
Abstract:
Fostering Engagement with Health and Housing Innovation: Development of Participant Personas in a Social Housing Cohort (Preprint)
. BACKGROUND
. Personas, based on customer or population data, are widely used to inform design decisions in the commercial sector. The variety of methods available means that personas can be produced from projects of different types and scale.
.
.
. OBJECTIVE
. This study aims to experiment with the use of personas that bring together data from a survey, household air measurements and electricity usage sensors, and an interview within a research and innovation project, with the aim of supporting eHealth and eWell-being product, process, and service development through broadening the engagement with and understanding of the data about the local community.
.
.
. METHODS
. The project participants were social housing residents (adults only) living in central Cornwall, a rural unitary authority in the United Kingdom. A total of 329 households were recruited between September 2017 and November 2018, with 235 (71.4%) providing complete baseline survey data on demographics, socioeconomic position, household composition, home environment, technology ownership, pet ownership, smoking, social cohesion, volunteering, caring, mental well-being, physical and mental health–related quality of life, and activity. K-prototype cluster analysis was used to identify 8 clusters among the baseline survey responses. The sensor and interview data were subsequently analyzed by cluster and the insights from all 3 data sources were brought together to produce the personas, known as the Smartline Archetypes.
.
.
. RESULTS
. The Smartline Archetypes proved to be an engaging way of presenting data, accessible to a broader group of stakeholders than those who accessed the raw anonymized data, thereby providing a vehicle for greater research engagement, innovation, and impact.
.
.
. CONCLUSIONS
. Through the adoption of a tool widely used in practice, research projects could generate greater policy and practical impact, while also becoming more transparent and open to the public.
.
Abstract.
Maier M, Mueller M, Yan X (In Press). Introducing a Localised Spatio-temporal LCI Method with wheat production as exploratory case study. Journal of Cleaner Production
2023
Menneer T, Mueller M, Townley S (2023). A cluster analysis approach to sampling domestic properties for sensor deployment. Building and Environment, 231, 110032-110032.
Robayo M, Mueller M, sharkh S, Abusara M (2023). Assessment of Supercapacitor performance in a hybrid energy storage system with an energy management based on the discrete wavelet transform. Journal of Energy Storage
Alrashedi Y (2023). Localised vs. Centralised Management of Spatially Distributed Populations.
Abstract:
Localised vs. Centralised Management of Spatially Distributed Populations
We consider management strategies for spatially distributed natural populations.
The thesis considers two types of dynamical systems modelling approaches: rstly,
population projection matrix models for spatially distributed meta-populations, and
secondly, integral projection models.
The rst approach combines localised observation and adaptive control strategies
with information sharing to manage the dynamics of meta-populations e ectively.
We consider meta-populations of N 2 N locally distinct equivalent stage-structured
populations that are coupled via dispersal of one or more stages. Dispersal is modelled
through a directed graph on the set of N nodes. This directional dispersal allows
for wind-born dispersal, e.g. of seed stages, or nearest neighbour dispersal of stages
able to disperse between di erent locations. Information sharing is captured by a
second directed graph on the set of N nodes. This directional information sharing
allows modelling of communication between the nodes, e.g. farmers sharing pesticide
application strategies via a preferential attachment network. The novelty lies in the
use of information sharing between managers of neighbouring populations, which acts
to anticipate potential outbreaks. We explore situations when information sharing is
and is not matched with dispersal. Information sharing improves the outcomes in
that the size and extent of a pest outbreak and the amount of pesticide sprayed is
reduced.
Second, integral projection models (IPMs) can be used as models for spatio-temporal
processes. Here we borrow ideas from Kot et al. [1], who use IPMs to model spatially
distributed biological invasions. The speed of the biological invasion is a key property
which may act as a proxy for the damage caused by the pest. The speed of invasion,
or invasive wave speed, in the IPM depends on the form of the IPM kernel, for example, Gaussian or exponential distributions. These kernels depend on parameters
which control the per-time-step spread of the pest. Parameters yielding narrower
kernels lead to slower speed of spread. Now suppose we want to reduce the speed of
spread (aka damage) to some below some pre-determined threshold. Assuming that
increasing volume of pesticide narrows the kernel, we propose an adaptive algorithm
which drives the speed to below the set threshold using an estimate of current speed.
We apply our results to the control of invasion speed in D.pseudoobscura.
Abstract.
2022
Alharthi M, Hughes T, Mueller M (2022). Optimal Control of Volterra Difference Equations of the First Kind.
Abstract:
Optimal Control of Volterra Difference Equations of the First Kind
Abstract.
Walker T, Menneer T, Tu G, Mueller M, Leyshon C, Leyshon M, Morrissey K, Bland E, Buckingham S (2022). P44 Smarter social housing: user perspectives on technology adoption for healthy homes. Society for Social Medicine Annual Scientific Meeting Abstracts.
Robayo M (2022). Real-time Energy Management System of Battery-Supercapacitor in Electric vehicles.
Abstract:
Real-time Energy Management System of Battery-Supercapacitor in Electric vehicles
This thesis presents the design, simulation and experimental validation of an Energy Management System (EMS) for a Hybrid Energy Storage System (HESS) composed of lithium ion batteries and Supercapacitors (SCs) in electric vehicles. The aim of the EMS is to split the power demand considering the weaknesses and strengths or the power sources. The HESS requires an EMS to determine power missions for the battery and SC in real time, where the SC is commanded to assist the battery during high power demand and recover the energy generated during braking. Frequency sharing techniques have been proposed by researchers to achieve this objective, including the Discrete Wavelet Transform (DWT) and conventional filtration methods (low and high pass filters). However, filtration approaches can introduce delay (milliseconds to tens of seconds) in the frequency components which undermines the hybridisation advantages. Hence, the selection of the filtration technique and filter design are crucial to the system's performance. Researchers have proposed power demand prediction methodologies to deal with time delay, however, the advantages and drawbacks of using such methods have not been investigated thoroughly, particularly whether time delay compensation and its inherent prediction error improves the system performance, efficiency, and timely SC contribution during the motoring and braking stages. This work presents a fresh perspective to this research field by introducing a novel approach that deals with delay without complicated prediction algorithms and improves the SC contribution during the motoring and braking stages while reducing energy losses in the system.
The proposed EMS allows the SC to provide timely assistance during motoring and to recover the braking energy generated. A charging strategy controls energy circulation between the battery and SC to keep the SC charge availability during the whole battery discharge cycle. The performance and efficiency of the HESS is improved when compared to the traditional use of conventional filtration techniques and the DWT. Results show that the proposed EMS method improves the energy efficiency of the HESS. For the US06 driving cycle, the energy efficiency is 91.6%. This is superior to the efficiency obtained with an EMS based on a high pass filter (41.3%), an EMS based on DWT high frequency component (30.3%) and an EMS based on the predicted DWT high frequency component (41%).
Abstract.
Walker T, Menneer T, Tu G, Mueller M, Leyshon C, Leyshon M, Morrissey K, Bland E (2022). Smarter social housing: user perspectives on technology adoption for healthy homes and health equity. European Health Economics Association: Health economics for sustainable welfare systems. 5th - 8th Jul 2022.
Abstract:
Smarter social housing: user perspectives on technology adoption for healthy homes and health equity
Abstract.
2021
Menneer T, Qi Z, Taylor T, Paterson C, Tu G, Elliott LR, Morrissey K, Mueller M (2021). Changes in Domestic Energy and Water Usage during the UK COVID-19 Lockdown Using High-Resolution Temporal Data.
International Journal of Environmental Research and Public Health,
18(13), 6818-6818.
Abstract:
Changes in Domestic Energy and Water Usage during the UK COVID-19 Lockdown Using High-Resolution Temporal Data
In response to the COVID-19 outbreak, the UK Government provided public health advice to stay at home from 16 March 2020, followed by instruction to stay at home (full lockdown) from 24 March 2020. We use data with high temporal resolution from utility sensors installed in 280 homes across social housing in Cornwall, UK, to test for changes in domestic electricity, gas and water usage in response to government guidance. Gas usage increased by 20% following advice to stay at home, the week before full lockdown, although no difference was seen during full lockdown itself. During full lockdown, morning electricity usage shifted to later in the day, decreasing at 6 a.m. and increasing at midday. These changes in energy were echoed in water usage, with a 17% increase and a one-hour delay in peak morning usage. Changes were consistent with people getting up later, spending more time at home and washing more during full lockdown. Evidence for these changes was also observed in later lockdowns, but not between lockdowns. Our findings suggest more compliance with an enforced stay-at-home message than with advice. We discuss implications for socioeconomically disadvantaged households given the indication of inability to achieve increased energy needs during the pandemic.
Abstract.
Williams AJ, Menneer T, Sidana M, Walker T, Maguire K, Mueller M, Paterson C, Leyshon M, Leyshon C, Seymour E, et al (2021). Fostering Engagement with Health and Housing Innovation: Development of Participant Personas in a Social Housing Cohort.
JMIR Public Health and Surveillance,
7(2), e25037-e25037.
Abstract:
Fostering Engagement with Health and Housing Innovation: Development of Participant Personas in a Social Housing Cohort
. Background
. Personas, based on customer or population data, are widely used to inform design decisions in the commercial sector. The variety of methods available means that personas can be produced from projects of different types and scale.
.
.
. Objective
. This study aims to experiment with the use of personas that bring together data from a survey, household air measurements and electricity usage sensors, and an interview within a research and innovation project, with the aim of supporting eHealth and eWell-being product, process, and service development through broadening the engagement with and understanding of the data about the local community.
.
.
. Methods
. The project participants were social housing residents (adults only) living in central Cornwall, a rural unitary authority in the United Kingdom. A total of 329 households were recruited between September 2017 and November 2018, with 235 (71.4%) providing complete baseline survey data on demographics, socioeconomic position, household composition, home environment, technology ownership, pet ownership, smoking, social cohesion, volunteering, caring, mental well-being, physical and mental health–related quality of life, and activity. K-prototype cluster analysis was used to identify 8 clusters among the baseline survey responses. The sensor and interview data were subsequently analyzed by cluster and the insights from all 3 data sources were brought together to produce the personas, known as the Smartline Archetypes.
.
.
. Results
. The Smartline Archetypes proved to be an engaging way of presenting data, accessible to a broader group of stakeholders than those who accessed the raw anonymized data, thereby providing a vehicle for greater research engagement, innovation, and impact.
.
.
. Conclusions
. Through the adoption of a tool widely used in practice, research projects could generate greater policy and practical impact, while also becoming more transparent and open to the public.
.
Abstract.
Menneer T, Mueller M, Sharpe RA, Townley S (2021). Modelling mould growth in domestic environments using relative humidity and temperature.
Building and EnvironmentAbstract:
Modelling mould growth in domestic environments using relative humidity and temperature
Damp and high levels of relative humidity (RH), typically above 70-80%, are known to provide mould-favourable conditions. Exposure to indoor mould contamination has been associated with an increased risk of developing and/or exacerbating a range of allergic and non-allergic diseases. The VTT model is a mathematical model of indoor mould growth that was developed based on surface readings of RH and temperature on wood in a controlled laboratory chamber. The model provides a mould index based on the environmental readings. We test the generalisability of this laboratory-based model to less-controlled domestic environments across different values of model parameters. Mould indices were generated using objective measurements of RH and temperature in the air, taken from sensors in a domestic setting every 3-5 minutes over 1 year in the living room and bedroom across 219 homes. Mould indices were assessed against self-reports from occupants regarding the presence of visible mould growth and mouldy odour in the home. Logistic regression provided evidence for relationships between mould indices and occupant responses. Mould indices were most successful at predicting occupant responses when the model parameters encouraged higher vulnerability to mould growth compared with the original VTT model. A lower critical RH level, above which mould grows, a higher sensitivity, and larger increases in the mould index all consistently increased performance. Using moment-to-moment time-series data for temperature and RH, the model and its developments could help inform smart monitoring or control of RH, for example to counter risks associated with reduced ventilation in energy efficient homes.
Abstract.
2020
Zheng L, Mueller M, Luo C, Yan X (2020). A Review of Data-driven Approaches for Occupant’s Behaviour in Building Energy Conservation. Applied Energy Symposium 2020: Low carbon cities and urban energy systems. 10th - 17th Oct 2020.
Abstract:
A Review of Data-driven Approaches for Occupant’s Behaviour in Building Energy Conservation
Abstract.
Robayo M, Abusara M, Mueller M, Sharkh S (2020). A Smart Energy Management System for Battery-Supercapacitor in Electric Vehicles based on the Discrete Wavelet Transform and Deep Learning.
Abstract:
A Smart Energy Management System for Battery-Supercapacitor in Electric Vehicles based on the Discrete Wavelet Transform and Deep Learning
Abstract.
Walker T, Menneer T, Leyshon C, Leyshon M, Williams AJ, Mueller M, Taylor T (2020). Determinants of Volunteering Within a Social Housing Community.
VOLUNTAS: International Journal of Voluntary and Nonprofit Organizations,
33(1), 188-200.
Abstract:
Determinants of Volunteering Within a Social Housing Community
AbstractIn general, research demonstrates that deprivation, education, health, and well-being are determinants of volunteering, and that volunteering can play an important role in building stronger communities and provides many benefits for individual health and well-being. This study concentrates on the effects of physical and mental health and well-being as predictors when the aspect of socio-economic impact has been minimised. It utilises a unique data set from a UK Housing Association community with generally high levels of deprivation. Data were analysed using bivariate probit regression. In contrast to previous findings, physical health and mental health were not significantly related to volunteering. The key finding was that mental well-being was significantly related to informal volunteering.
Abstract.
Jones O, Ezard THG, Dooley C, Healy K, Hodgson D, Mueller M, Townley S, Salguero-Gómez R (2020). My family and other animals: Human demography under a comparative cross-species lens. In Burger O, Lee R, Sear R (Eds.)
Human Evolutionary Demography, Open Science Framework.
Abstract:
My family and other animals: Human demography under a comparative cross-species lens
Abstract.
Williams A, Menneer T, Sidani M, Walker T, Maguire K, Mueller M, Paterson C, Leyshon M, Leyshon C, Seymour E, et al (2020). Using machine learning clustering techniques to support the understanding of populations and inform action. Public Health England Research and Science Conference - Application of scientific methods to improve and protect health.
Abstract:
Using machine learning clustering techniques to support the understanding of populations and inform action
Abstract.
2019
Faÿ F-X, Henriques JC, Kelly J, Mueller M, Abusara M, Sheng W, Marcos M (2019). Comparative assessment of control strategies for the biradial turbine in the Mutriku OWC plant. Renewable Energy, 146, 2766-2784.
2018
Nicol‑Harper A, Dooley C, Packman D, Mueller M, Bijak J, Hodgson D, Townley S, Ezard T (2018). Inferring transient dynamics of human populations from matrix non-normality. Population Ecology
Faÿ F-X, Kelly J, Henriques J, Pujana A, Abusara M, Mueller M, Touzon I, Ruiz-Minguela P (2018). Numerical Simulation of Control Strategies at Mutriku Wave Power Plant. ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering. 17th - 22nd Jun 2018.
Abstract:
Numerical Simulation of Control Strategies at Mutriku Wave Power Plant
Abstract.
Faÿ F-X, Kelly J, Henriques J, Pujana A, Abusara M, Mueller M, Touzon I, Ruiz-Minguela P (2018). Numerical Simulation of Control Strategies at Mutriku Wave Power Plant. ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering. 17th - 22nd Jun 2018.
2017
Maier M, Mueller M, Yan X (2017). Introduction of a spatiotemporal Life Cycle Inventory method using a wind energy example.
Abstract:
Introduction of a spatiotemporal Life Cycle Inventory method using a wind energy example
Abstract.
2016
Guiver C, Mueller M, Hodgson D, Townley S (2016). Robust set-point regulation for ecological models with multiple management goals.
J Math Biol,
72(6), 1467-1529.
Abstract:
Robust set-point regulation for ecological models with multiple management goals.
Population managers will often have to deal with problems of meeting multiple goals, for example, keeping at specific levels both the total population and population abundances in given stage-classes of a stratified population. In control engineering, such set-point regulation problems are commonly tackled using multi-input, multi-output proportional and integral (PI) feedback controllers. Building on our recent results for population management with single goals, we develop a PI control approach in a context of multi-objective population management. We show that robust set-point regulation is achieved by using a modified PI controller with saturation and anti-windup elements, both described in the paper, and illustrate the theory with examples. Our results apply more generally to linear control systems with positive state variables, including a class of infinite-dimensional systems, and thus have broader appeal.
Abstract.
Author URL.
Guiver C, Edholm C, Jin Y, Mueller M, Powell J, Rebarber R, Tenhumberg B, Townley S (2016). Simple Adaptive Control for Positive Linear Systems with Applications to Pest Management. SIAM Journal on Applied Mathematics, 76(1), 238-275.
2013
Rüffer BS, Van De Wouw N, Mueller M (2013). Convergent systems vs. incremental stability.
Systems and Control Letters,
62(3), 277-285.
Abstract:
Convergent systems vs. incremental stability
Two similar stability notions are considered; one is the long established notion of convergent systems, the other is the younger notion of incremental stability. Both notions require that any two solutions of a system converge to each other. Yet these stability concepts are different, in the sense that none implies the other, as is shown in this paper using two examples. It is shown under what additional assumptions one property indeed implies the other. Furthermore, this paper contains necessary and sufficient characterizations of both properties in terms of Lyapunov functions. © 2012 Elsevier B.V. All rights reserved.
Abstract.
Hackl CM, Hopfe N, Ilchmann A, Mueller M, Trenn S (2013). FUNNEL CONTROL FOR SYSTEMS WITH RELATIVE DEGREE TWO.
SIAM JOURNAL ON CONTROL AND OPTIMIZATION,
51(2), 965-995.
Author URL.
2012
Ruffer BS, Van De Wouw N, Mueller M (2012). From convergent dynamics to incremental stability. Proceedings of the IEEE Conference on Decision and Control, 2958-2963.
Li G, Weiss G, Mueller M, Townley S, Belmont MR (2012). Wave energy converter control by wave prediction and dynamic programming.
Renewable Energy,
48, 392-403.
Abstract:
Wave energy converter control by wave prediction and dynamic programming
We demonstrate that deterministic sea wave prediction (DSWP) combined with constrained optimal control can dramatically improve the efficiency of sea wave energy converters (WECs), while maintaining their safe operation. We focus on a point absorber WEC employing a hydraulic/electric power take-off system. Maximizing energy take-off while minimizing the risk of damage is formulated as an optimal control problem with a disturbance input (the sea elevation) and with both state and input constraints. This optimal control problem is non-convex, which prevents us from using quadratic programming algorithms for the optimal solution. We demonstrate that the optimum can be achieved by bang-bang control. This paves the way to adopt a dynamic programming (DP) algorithm to resolve the on-line optimization problem efficiently. Simulation results show that this approach is very effective, yielding at least a two-fold increase in energy output as compared with control schemes which do not exploit DSWP. This level of improvement is possible even using relatively low precision DSWP over short time horizons. A key finding is that only about 1 second of prediction horizon is required, however, the technical difficulties involved in obtaining good estimates necessitate a DSWP system capable of prediction over tens of seconds. © 2012 Elsevier Ltd.
Abstract.
2010
Mueller M, Cantoni M (2010). Normalized coprime representations for time-varying linear systems. appears: Proc. 49th IEEE Conf. Decis. Control.
Abstract:
Normalized coprime representations for time-varying linear systems
Abstract.
Ilchmann A, Mueller M (2010). Robustness of funnel control in the gap metric. appears: Proc. 49th IEEE Conf. Decis. Control.
Abstract:
Robustness of funnel control in the gap metric
Abstract.
2009
Mueller M (2009). Normal form for linear systems with respect to its vector relative degree.
Linear Algebra and its Applications,
430(4), 1292-1312.
Abstract:
Normal form for linear systems with respect to its vector relative degree
For multi-input multi-output (MIMO) linear systems with existing vector relative degree a normal form is constructed. This normal form is not only structural simple but allows to characterize the system's zero dynamics for the design of feedback controllers. A characterization of the zero dynamics in terms of the normal form is given.
Abstract.
Mueller M (2009). Output Feedback Control and Robustness in the Gap Metric.
French M, Ilchmann A, Mueller M (2009). Robust stabilization by linear output delay feedback.
SIAM J. Control Optim.,
48(4), 2533-2561.
Abstract:
Robust stabilization by linear output delay feedback
The main result establishes that if a controller C (comprising of a linear feedback of the output and its derivatives) globally stabilizes a (nonlinear) plant P, then global stabilization of P can also be achieved by an output feedback controller C[h] where the output derivatives in C are replaced by an Euler approximation with sufficiently small delay h > 0. This is proved within the conceptual framework of the nonlinear gap metric approach to robust stability. The main result is then applied to finite dimensional linear minimum phase systems with unknown coefficients but known relative degree and known sign of the high frequency gain. Results are also given for systems with non-zero initial conditions.
Abstract.
Ilchmann A, Mueller M (2009). Robustness of funnel control in the gap metric.
SIAM J. Control Optim.,
48(5), 3169-3190.
Abstract:
Robustness of funnel control in the gap metric
For m-input, m-output, finite-dimensional, linear systems satisfying the classical assumptions of adaptive control (i.e. (i) minimum phase, (ii) relative degree one and (iii) positive high-frequency gain), the well known funnel controller k(t) = φ(t)/(
1−φ(t)|e(t)|) , u(t) = −k(t)e(t) achieves output regulation in the following sense: all states of the closed-loop system are bounded and, most importantly, transient behaviour of the tracking error e = y − y_ref is ensured such that the evolution of e(t) remains in a performance funnel with prespecified boundary 1/φ(t), where y_ref denotes a reference signal bounded with essentially bounded derivative. As opposed to classical adaptive high-gain output feedback, system identification or internal model is not invoked and the gain k(·) is not
monotone.
Invoking the conceptual framework of the nonlinear gap metric we show that the funnel controller is robust in the following sense: the funnel controller copes with bounded input and output disturbances and, more importantly, it may even be applied to a system not satisfying any of the classical conditions (i)–(iii) as long as the initial conditions and the disturbances are “small” and the system is “close” (in terms of a “small” gap) to a system satisfying (i)–(iii).
Abstract.
Ilchmann A, Mueller M (2009). Robustness of λ-tracking and funnel control in the gap metric. Proc. Joint 48th IEEE Conf. Decis. Control and 28th Chinese Contr. Conf.
Abstract:
Robustness of λ-tracking and funnel control in the gap metric
Abstract.
2008
Ilchmann A, Mueller M (2008). Robustness of λ-tracking in the gap metric.
SIAM J. Control Optim.,
47(5), 2724-2744.
Abstract:
Robustness of λ-tracking in the gap metric
For m-input, m-output, finite-dimensional, linear systems satisfying the classical assumptions of adaptive control (i.e. (i) minimum phase, (ii) relative degree one and (iii) "positive" high-frequency gain), it is well known that the adaptive λ-tracker 'u = -ke, k' = max{0; |e|-λ}|e|' achieves λ-tracking of the tracking error e if applied to such a system: all states of the closed-loop system are bounded and |e| is ultimately bounded by λ, where λ > 0 is prespecified and may be arbitrarily small.
Invoking the conceptual framework of nonlinear gap metric, we show that the λ-tracker is robust. In the present setup this means in particular that the λ-tracker copes with bounded input and output disturbances and, more importantly, it may even be applied to a system not satisfying any of the classical conditions (i)-(iii) as long as the initial conditions and the disturbances are "small" and the system is "close" (in terms of "small" gap) to a system satisfying (i)-(iii).
Abstract.
2007
Ilchmann A, Mueller M (2007). Time-varying linear systems: relative degree and normal form.
IEEE Trans. Aut. Control,
52(5), 840-851.
Abstract:
Time-varying linear systems: relative degree and normal form
We define the relative degree of time-varying linear systems, show that it coincides with Isidori’s and with Liberzon/Morse/Sontag’s definition if the system is understood as a time-invariant nonlinear system, characterize it in terms of the system data and their derivatives, derive a normal form with respect to a time-varying linear coordinate transformation, and finally characterize the zero dynamics.
Abstract.
2005
Mueller M (2005). A normal form for time-varying linear systems.
Abstract:
A normal form for time-varying linear systems
There are several types of characterisations of the so-called relative degree for time-invariant input output systems. Well known concepts for relative degree exist for time-varying linear and nonlinear systems. This diploma thesis gives a generalised definition of relative degree for time-varying nonlinear systems. This definition is used to establish a characterisation of relative degree for time-varying linear systems in terms of the time-varying system matrices and their derivatives. It will be proved that if time-invariant linear systems are considered, then the description for time-varying linear systems results in the well known characterisation of relative degree for time-invariant linear systems, and, if the time-varying linear system is interpreted as time-invariant nonlinear system, then the definition of relative degree is assured. The main result of this work is, that the characterisation of relative degree for time-varying linear systems will be used to derive a normal form for this systems concerning time-varying linear coordinate transformation. These normal form is similar to the normal form of time-invariant linear systems.
Finally the normal form for time-varying linear systems is used to consider the so-called zero dynamics of this systems. Boundedness and stability for the zero dynamics will be defined and it will be shown that a time-varying linear system has bounded zero dynamics if, and only if, the zero dynamics of the corresponding normal form are bounded.
Abstract.
Mueller M (2005). Lemmata zum Hurwitz-Kriterium.