LQR technique based SMC design for a class of uncertain time-delay Conic nonlinear systems

In this paper, the finite-time sliding mode controller design problem of a class of conic-type nonlinear systems with time-delays, mismatched external disturbance and uncertain coefficients is investigated. The time-delay conic nonlinearities are considered to lie in a known hypersphere with an uncertain center. Conditions have been obtained to design a linear quadratic regulator based on sliding mode control. For this purpose, by applying Lyapunov- Krasovskii stability theory and linear matrix inequality approach, sufficient conditions are derived to ensure the finite-time boundedness of the closed-loop systems over the finite-time interval. Thereafter, an appropriate control strategy is constructed to drive the state trajectories onto the specified sliding surface in a finite time. Finally, an example related to the time-delayed Chua’s circuit is given to demonstrate the effectiveness of the suggested method. Also, the efficiency of the suggested method is compared with other methods by using an another numerical example