This paper considers a global sliding mode control (GSMC) approach for the stabilization of uncertain chaotic systems with multiple delays and input nonlinearities. By designing the global sliding mode surface, the offered scheme eliminates reaching phase problem. The offered control law is formulated based on state estimation, Lyapunov–Krasovskii stability theory, and linear matrix inequality (LMI) technique which present the asymptotic stability conditions. Moreover, the proposed design approach guarantees the robustness against multiple delays, nonlinear inputs, nonlinear functions, external disturbances, and parametric uncertainties. Simulation results for the presented controller demonstrate the efficiency and feasibility of the suggested procedure.
This paper proposes the observer design method for linear and nonlinear singular discrete-time systems with constant time delays. 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 r LMI r toolbox. The su cient 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 the observer design of a singular linear system with a time-varying delay is presented. Simulation results are included to prove the e ciency of the suggested approach.
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