Robust H∞ Sliding Mode Controller Design of a Class of Time-Delayed Discrete Conic-Type Nonlinear Systems

This paper studies the H ∞ sliding mode control (SMC) problem for a class of discrete-time conictype nonlinear systems with time-delays and uncertainties. The nonlinear terms satisfy the conic-type constraint condition that lies in a know hyper-sphere with an uncertain center. By choosing a proper Lyapunov candidate, sufficient conditions are derived to ensure the asymptotic stability of the sliding mode dynamics while achieving a prescribed H ∞ disturbance attenuation level and finally converted into a minimization problem. The controller is constructed to guarantee the discrete-time reach condition and maintain the states on the prespecified sliding surface. A simulation result and a practical example related to the Chua's circuit are given at last to show the validity of our SMC strategy.