Fuzzy decentralized variable structure tracking control with optimal and improved robustness designs for nonlinear interconnected systems

This paper considers a nonlinear interconnected system which contains N subsystems. Each of the subsystems is approximated by the weighted combination of L linear pulse transfer function systems (LPTFSs). For every ideal LPTFS of the ith subsystem, a dead-beat to its switching surface is first designed t is called "variable structure tracking control". The output disturbance of the mth LPTFS includes the interconnections coming from the other subsystems, the approximation error of the ith subsystem, and the interactions resulting from the other LPTFSs. In general, the corresponding output disturbance is not small and contains various frequencies. Under the circumstances, the H^∞-norm of the weighted sensitivity function between the mth switching surface and the output disturbance is minimized. It is the so-called "optimal robustness", that is, the first aspect of the robustness design of the fuzzy decentralized variable structure tracking control. A suitable selection of the weighting function for the sensitivity function can reject the corresponding output disturbance. Although the effect of the output disturbance is attenuated and approximately rejected, a better performance can be improved by a fuzzy switching control which is based on the Lyapunov redesign. This is the second feature for the robustness design that is called as "improved robustness". The stability of the overall system is verified by the Lyapunov stability theory. Simulations are also given to illustrate the design procedure and verify the usefulness of the proposed control scheme.