A fuzzy decentralized variable structure tracking control with optimal and improved robustness designs: theory and applications

To begin with, each subsystem of a nonlinear interconnected system was approximated by a weighted combination of L linear pulse transfer function systems (LPTFSs). For every nominal LPTFS of the mth subsystem, a dead-beat to its switching surface was first designed. The output disturbance of the mth LPTFS included the interconnections coming from the other subsystems, the approximation error of the mth subsystem, and the interactions resulting from the other LPTFSs. In general, this output disturbance was not small and contains various frequencies. Under this circumstances, the H^∞-norm of the weighted sensitivity function between the mth switching surface and its corresponding output disturbance was minimized. In addition, an appropriate selection of the weighted function for the sensitivity could reject the corresponding mode of the output disturbance. Although the effect of the output disturbance is attenuated and partially rejected, a better performance could be enhanced by a switching control based on the Lyapunov redesign. In addition, the stability of the overall system was verified by Lyapunov stability theory. The simulations for the LPTFSs with different delays or nonminimum phases or unstable features were arranged to evaluate the effectiveness of the proposed control. Finally, the application to the trajectory tracking of the robot arm including the fuzzy modeling was carried out to confirm the practicality of the proposed control.