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The robust stabilization problem for a family of nonlinear plants with mismatch uncertainties is addressed,and a solution is presented based on variable structure control theory and H∞ control theory.A kind of boundary layer is built near the ideal switch surface which can eliminate chattering in the switch surface.The proposed control method with L2 gain can guarantee exponential stability of a system state with no parameter uncertainty and external disturbance,while it can guarantee state ultimate boundness if parameter uncertainty and external disturbance exist.In the proposed design method,stability of the closed-loop system is analyzed by adopting the Lyapunov function approach.Finally the numerical simulation results show that the proposed smooth variable structure controller has good performance without chattering in the switch surface.
The robust stabilization problem for a family of nonlinear plants with mismatch uncertainties is addressed, and a solution is presented based on variable structure control theory and H∞ control theory. A kind of boundary layer is built near the ideal switch surface which can eliminate chattering in the switch surface.The proposed control method with L2 gain can guarantee exponential stability of a system state with no parameter uncertainty and external disturbance, while it can guarantee the ultimate boundness if parameter uncertainty and external disturbance exist. the proposed design method, stability of the closed-loop system is analyzed by adopting the Lyapunov function approach. Finally the numerical simulation results show that the proposed smooth variable structure controller has good performance without chattering in the switch surface.