An LMI approach to L2 gain analysis and control synthesis of switched systems

This paper investigates the L₂ gain analysis and control synthesis of discrete-time switched systems under arbitrary switching by linear matrix inequality (LMI) approach together with switched Lyapunov function method. First, the existence of a switched Lyapunov function is proven to be equivalent to the feasibility of some LMIs. An upper bound of the L₂ gain for switched systems can be computed by solving an eigenvalue problem (EVP). Then, we design a switched state feedback controller and a switched output feedback controller, respectively, guaranteeing that the corresponding closed-loop system is asymptotically stable with an L₂ gain smaller than a fixed constant. LMI-based conditions for both cases are presented. Finally, two examples are given to illustrate our results.