Nonfragile Observer for Discrete-Time Switched Nonlinear Systems with Time Delay

This paper investigates the problem of the nonfragile observer design for discrete-time switched nonlinear systems with time delay. Based on the average dwell-time approach and linear matrix inequality (LMI) techniques, an exponential stability criterion for the discrete-time switched delay system with Lipschitz nonlinearity is derived. Based on several technical lemmas, the discrete-time observer design can be transferred to the problem of solving a set of LMIs. Furthermore, in cases when the gain of the state observer varies, a kind of nonfragile observer is proposed, and the solution to the observer gain is also obtained by solving a set of LMIs. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.