Switched Linear Differential Systems: an introduction

In switched systems, different dynamical regimes are triggered depending on the value of a switching signal. Traditionally, such systems are modeled with state space representations sharing the same state space. However, several reasons suggest that other, more general types of representations ought to be used. Among these are parsimony (using as few equations and variables as possible) and modularity (incremental modification of existing models) that are of paramount importance in, for example, modelling and analysing power grids. 

These considerations led Paolo Rapisarda and Professor Jonathan Carlos Mayo-Maldonado to develop a framework in which the different dynamical regimes are represented by systems of constant-coefficient linear differential equations. At the switching instants, the trajectories of such systems and their derivatives must satisfy “gluing conditions” that characterise physical conditions for concatenation. In their approach, the dynamical modes do not necessarily share the same state space.  

In this talk, Paolo Rapisarda will illustrate some of the basic features of this framework, discuss stability and dissipativity, and illustrate some applications in modelling and analysis of power systems.