Robust stability and stabilization for nonlinear uncertain discrete-time descriptor switched systems

In this paper, the robust stability and robust state feedback stabilization problems for a class of nonlinear discrete-time descriptor switched systems with parameter uncertainties are discussed. First, based on Lyapunov theory and the existence theorem of hidden function, a linear matrix inequality (LMI) sufficient condition is developed which guarantees that the nonlinear discrete-time descriptor switched systems are regular, causal, have unique solution in a neighborhood of the origin, and are uniformly asymptotically stable. Then, with this condition, a robust stability condition for uncertain systems is obtained, and the design method of robust state feedback controllers is given. Last, a numerical example is provided to illustrate the effectiveness of the proposed methods.