Quadratic Stabilization with an H∞-Norm Bound for Linear Discrete-Time Switched Systems

The problem of quadratic stabilization with an H
∞
-norm bound is studied for a class of linear discrete-time switched systems in this paper. Under the assumption that none of subsystems is quadratically stabilizable with an H
∞
-norm bound, by using single Lyapunov function method, a sufficient condition for quadratic stabilization with an H
∞
-norm bound is derived via a state-based switching law. The switching state feedback controller and switching law are also given. We show this sufficient condition is also necessary if the number of subsystems is two. Finally, a simulation example is given to illustrate the validity of the results.