Delay-dependent T-S fuzzy control for nonlinear interconnected systems: Using dithers as auxiliaries

In this study, a novel approach via the composite of fuzzy controllers and dithers is presented. According to this approach, we can synthesize a set of fuzzy controllers and find appropriate dithers to stabilize nonlinear multiple time-delay (NMTD) interconnected systems. A robustness design of model-based fuzzy control is first proposed to overcome the effect of modeling errors between the NMTD interconnected subsystems and Takagi-Sugeno (T-S) fuzzy models. In terms of Lyapunov's direct method, a delay-dependent stability criterion is then derived to guarantee the asymptotic stability of NMTD interconnected systems. Based on this criterion and the decentralized control scheme, a set of model-based fuzzy controllers is synthesized via the technique of parallel distributed compensation (PDC) to stabilize the NMTD interconnected system. When the designed fuzzy controllers cannot stabilize the NMTD interconnected systems, a batch of high-frequency signals (commonly referred to as dithers) is simultaneously introduced to stabilize it. If the frequencies of dithers are high enough, the outputs of the dithered interconnected system and those of its corresponding mathematical model-the relaxed interconnected system can be made as close as desired. This makes it possible to obtain a rigorous prediction of the stability of the dithered interconnected system based on the one of the relaxed interconnected system. Finally, a numerical example is given to illustrate the feasibility of our approach.