H ∞ sliding mode observer design for a class of nonlinear discrete time‐delay systems: A delay‐fractioning approach

SUMMARY In this paper, the H  ∞  sliding mode observer (SMO) design problem is investigated for a class of nonlinear discrete time‐delay systems. The nonlinear descriptions quantify the maximum possible derivations from a linear model, and the system states are allowed to be immeasurable. Attention is focused on the design of a discrete‐time SMO such that the asymptotic stability as well as the H  ∞  performance requirement of the error dynamics can be guaranteed in the presence of nonlinearities, time delay and external disturbances. Firstly, a discrete‐time discontinuous switched term is proposed to make sure that the reaching condition holds. Then, by constructing a new Lyapunov–Krasovskii functional based on the idea of ‘delay fractioning’ and by introducing some appropriate free‐weighting matrices, a sufficient condition is established to guarantee the desired performance of the error dynamics in the specified sliding mode surface by solving a minimization problem. Finally, an illustrative example is given to show the effectiveness of the designed SMO design scheme. Copyright © 2011 John Wiley & Sons, Ltd.