H∞ control for a class of non-minimum phase switched systems

In this paper, we study H_∞ control for a class of cascade non-minimum phase switched nonlinear systems. When arbitrary subsystem´s H_∞ control problem is not solvable, we design state feedback controllers and switching laws by using structural properties to guarantee both internal stability of the resulting closed-loop systems and prescribed L2-gain from disturbance input to the controlled output by using multiple Lyapunov function technique. A sufficient condition for the problem to be solvable is attributed to solving lower-dimension partial differential inequalities. These methods do not rely on the solutions of Hamilton-Jacobi inequalities.