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

This paper studies the H-infinity 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-infinity 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.

Automated summary

This paper investigates H-infinity sliding mode control for discrete-time conic-type nonlinear systems with time-delays and uncertainties. By selecting an appropriate Lyapunov candidate, conditions for asymptotic stability and disturbance attenuation are derived. The controller ensures system stability and sliding mode dynamics, as demonstrated by simulation results and a practical example.