Rejected, optimal and reinforced robustness designs of fuzzy variable structure control for a class of nonlinear discrete-time systems

A nonlinear discrete-time system is approximated by N subsystems described by pulse transfer functions. The approximation error between the nonlinear discrete-time system and the fuzzy linear pulse transfer function system is represented by the additive nonlinear time-varying uncertainties in every subsystem. First, a dead-beat to the switching surface for every ideal subsystem is designed. If part of the approximation error can be modeled as a known pulse transfer function for output disturbance, a controller based on the "internal model principle" is given to reject the corresponding disturbance. It is called "rejected robustness". Then the H_∞-norm of the transfer function between switching surface and the remaining output disturbance, the interaction caused by the other subsystem, is minimized. It is the so-called "optimal robustness" for robust control. Although the effect of the remaining output disturbance and the interaction is attenuated, a better performance can be reinforced by a switching control which is based on the Lyapunov redesign. This is the third step for the robustness design of control, which is called "reinforced robustness"