Optimal ∞ fuzzy control for nonlinear multiple time-delay interconnected systems: Using dithers as auxiliaries

This paper presents an effective approach to stabilize nonlinear multiple time-delay (NMTD) interconnected systems via a composite of fuzzy controllers and dithers. First, a neural-network (NN) model is employed to approximate each subsystem. Then, the dynamics of the NN model is converted into a linear differential inclusion (LDI) state-space representation. Next, in terms of Lyapunovs direct method, a delay-dependent stability criterion is derived to guarantee the exponential stability of the NMTD interconnected system. Subsequently, the stability conditions of this criterion are reformulated into a linear matrix inequality (LMI). Based on the LMI, a robustness design of fuzzy control is synthesized not only to stabilize the NMTD interconnected system but also to achieve the optimal ,performance by minimizing the disturbance attenuation level. A set of high-frequency signals (commonly referred to as dithers) is simultaneously injected to stabilize the NMTD interconnected system when the designed fuzzy controllers cannot stabilize it. If the dithers' frequencies 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 get a rigorous prediction of the stability of the dithered interconnected system by establishing the stability of the relaxed interconnected system. Finally, a numerical example with simulations is given to illustrate the feasibility of our approach.