Robust fuzzy controller design for nonlinear multiple time-delay systems by dithers

This study presents a robustness design of fuzzy control for nonlinear systems with multiple time delays. First, the neural-network (NN) model is employed to approximate the nonlinear multiple time-delay (NMTD) plant. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of the NN model. According to the LDI state-space representation, a robustness design of fuzzy control is proposed to overcome the effect of modeling errors between the NMTD plant and the NN model. If the designed fuzzy controller cannot stabilize the NMTD system, a dither, as an auxiliary of the fuzzy controller, is simultaneously introduced to stabilize the NMTD system. Based on the relaxed method, the NMTD system can be stabilized by regulating appropriately the parameters of dither. If the frequency of dither is high enough, the trajectory of the dithered system and that of its corresponding mathematical model—the relaxed system can be made as close as desired. This fact enables us to get a rigorous prediction of stability of the dithered system by establishing the stability of the relaxed system.