Abstract

Switched systems arise in many areas of physics and engineering, when different dynamical regimes are triggered depending on the value of a “switching rule”. In this talk, I will concentrate on systems that follow linear, time-invariant dynamics between one switching instant and the next.

Traditionally, such switched systems are modeled with state space representations sharing the same state space. However, several reasons suggest that other, more general types of representations could and should be used. These considerations led us to develop a framework in which the different dynamical regimes are represented by systems of higher-order constant-coefficient linear differential equations, together with “gluing conditions” specifying certain requirements on the trajectories at the switching instants. We call these “switched linear differential systems”.

In this talk I will illustrate some of the basic features of our approach, and discuss stability and dissipativity in this framework, including some applications in modelling and analysis of power electronics systems.