Abstract

In this paper, the observer design method for linear and nonlinear singular discrete-time systems with constant time-delays ‎is proposed. By constructing appropriate Lyapunov–Krasovskii functional and using linear matrix inequality (LMI) technique, ‎the asymptotic convergence criterion is developed in terms of LMIs, which can be solved numerically using MATLAB® LMI® ‎toolbox. The sufficient condition for the existence of a full-order observer is obtained and the states are estimated using ‎Schur complement and S-procedure lemma very well. Moreover, an extension procedure for observer design of singular ‎linear system with time-varying delay is presented. Simulation results are included to prove the efficiency of the suggested ‎approach.‎