H-infinity control for a class of switched nonlinear systems based on multiple Lyapunov functions

In this paper, we study H_∞ control for a class of switched nonlinear systems which are composed of a finite number of nonlinear cascade Minimum-phase subsystems. Each subsystem contains a zero-input asymptotically stable nonlinear part and a linearizable part. We exploit the Minimum-phase structural characteristic of the switched nonlinear systems to construct Multiple Lyapunov Functions, nonlinear controllers for all subsystems and a state-depend switching law. Conditions for the closed-loop system to have any given L2-gain with internal stability under designed switching laws are presented. These methods do not rely on the solutions of Hamilton-Jacobi inequalities.