An efficient observer design method for singular discrete-time systems with time delays and nonlinearity: LMI approach

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.