Advanced Lyapunov functions for Lur'e systems
Résumé
In this chapter, several problems of stability analysis of discrete-time (switched) nonlinear Lur'e systems are addressed. As a main contribution, a new class of (switched) Lyapunov functions that takes the cone sectors bounded nonlinearity into account and does not restrict its slope are proposed. Conditions for global and local stability analysis are presented in a different framework: in particular, when the switching law is arbitrary or a part of the control. For local stability analysis, an estimate of the basin of attraction is given by the unitary level set of the proposed Lyapunov function. A property of this set is that it may be non-convex and disconnected and less conservative than ellipsoidal sets. The chapter is peppered with illustrative examples.