Delay-Dependent Fuzzy Control for Nonlinear Multiple Time-Delay Large-scale Systems by Dithers: Neural-Network-Based Approach

In this study, the stabilization problem for nonlinear multiple time-delay large-scale systems is considered. First, a neural-network (NN) model is employed to approximate each interconnected subsystem. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of the NN model. Based on this LDI state-space representation, a robust fuzzy control design is proposed to overcome the effect of modeling errors between the nonlinear multiple time-delay large-scale systems and the NN models. Next, in terms of Lyapunov’s direct method, a delay-dependent criterion is derived in order to guarantee the stability (UUB) of nonlinear multiple time-delay large-scale systems. Subsequently, the stability conditions of this criterion are reformulated into linear matrix inequalities (LMIs). Based on the LMIs and the decentralized control scheme, a set of fuzzy controllers is then synthesized to stabilize the nonlinear large-scale system and the  H control performance is achieved at the same time. If the designed fuzzy controllers cannot stabilize the nonlinear large-scale system, a batch of dithers (as the auxiliaries of fuzzy controllers) is simultaneously introduced to stabilize the nonlinear large-scale system. The injection of high-frequency signals, commonly called dithers, into nonlinear systems may improve their performance. If the frequencies of the dithers are high enough, the outputs of the dithered large-scale system and those of its corresponding mathematical model—the relaxed large-scale system can be made as close as desired. This makes it possible to obtain a rigorous prediction of the stability of the dithered large-scale system by establishing that of the relaxed large-scale system. Finally, a numerical example with simulations is provided to illustrate the feasibility of our approach. Corresponding Author: F. H. Hsiao is with the Department of Electrical Engineering, National University of Tainan 33, Section 2, Shu Lin Street, Tainan 700, Taiwan, R.O.C. E-mail: [email protected] Manuscript received 22 Aug. 2012; revised 19 Feb. 2013; accepted 21 May 2013.