Standard H∞ Control for a Class State-Constrained Switched Systems With All Unstable Subsystems

This brief investigates the issue of the standard
$H_{\infty }$
control for state-constrained switched systems. The characteristics of the switched system are that its subsystems are internal unstable and the state is restricted within the unit hypercube. Firstly, the sufficient conditions for
$H_{\infty }$
control based on dwell time switching are given by using the multiple time-varying Lyapunov functions and the convex hull technique. Secondly, both the stability and the standard
$L_{2}$
-gain performance of the whole switched system are analyzed. Finally, an example is given to verify the effectiveness of the proposed method.