Stabilizability and robustness of switched linear systems: An aggregation approach

In this paper, we propose an approach for properly aggregating a wide class of switched linear systems which consist of continuous-time/discrete-time linear subsystems and switching devices that coordinate the switching among them. The aggregated systems are in a piecewise linear form which can be steered stable by an event-driven switching strategy. By investigating the aggregated systems, we develop a constructive switching design mechanism that simultaneously achieves exponential stability, and structural stability for the closed-loop system. The resultant stabilizing switching signals are mixed time-driven and event-driven, and are always well-defined.

I. Introduction

A switched linear system is a special hybrid system which consists of a set of linear continuous-time/discrete-time subsystems and a rule that orchestrates the switching among them. Switched systems are important from both theoretical and practical points of view. On one hand, switched systems represent a wide class of real-world systems with continuous-dynamics/discrte-event interactions. On the other hand, the hybrid control scheme provides an autonomous and intelligent framework for the analysis and control of complex systems.