A LMI approach to observer design for a class of switched nonlinear systems

The problem of state observer design is considered for discrete time delay switched systems with Lipschitz nonlinearity and random switching law. At first, based on multiple Lyapunov functions techniques, a sufficient condition for the convergence of switched error systems is presented. Furthermore, by matrix transformation techniques, observer gains can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, the simulation results show that the methods proposed in this paper is effective.