Stability analysis and observer design for discrete-time systems with interval time-varying delay

The problem of observer design for a class of nonlinear discrete‐time systems with time‐varying delay is considered. A new approach of nonlinear observer design is proposed for the class of systems. By using Lyapunov's stability theory and Schur complement lemma, the novel sufficient conditions that guarantee the observer error converge asymptotically to zero are obtained in terms of linear matrix inequalities. The computing method for observer gain matrix is given. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed method.