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. ? 2004 IEEE.EI