Robust State Feedback Stabilizability with a Quadratic Storage Function and Controller Switching

Abstract

In this chapter, we consider the problem of robust state feedback stabilizability with controller switching for a class of linear uncertain systems. The class of uncertain systems under investigation consists of linear time-varying systems with norm-bounded uncertainty. As in Chapter 2, we consider both asynchronous and synchronous controller switching. We introduce the concept of robust stabilizability via state feedback controller switching with a quadratic storage function. This notion is stronger than that of quadratic stabilizability from Chapter 2 and is closely related to the concept of dissipativity as in [47-49, 150]. We present a necessary and sufficient condition for robust stabilizability via asynchronous (synchronous) state feedback controller switching with a quadratic storage function. Furthermore, we derive a number of constructive sufficient conditions for robust stabilizability via controller switching that are based on the S-procedure approach of Chapter 2. Some of the main results of this chapter were originally published in [132].