New Approach on Robust and Reliable Decentralized Tracking Control for Fuzzy Interconnected Systems with Time-Varying Delay

This paper investigates the robust and reliable decentralized tracking control issue for the fuzzy large-scale interconnected systems with time-varying delay, which are composed of a number of T-S fuzzy subsystems with interconnections. Firstly, the ordinary fuzzy interconnected systems are equivalently transformed to the fuzzy descriptor systems; then, according to the Lyapunov direct method and the decentralized control theory of large-scale interconnected systems, the new linear matrix inequalities- (LMIs-) based conditions with some free variables are derived to guarantee the tracking performance not only when all control components are operating well, but also in the presence of some possible actuator failures. Moreover, there is no need for the precise failure parameters of the actuators, rather than the lower and upper bound. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed method. 1. Introduction Large-scale interconnected systems, such as electrical power systems, computer communication systems, economic systems, and process control systems, have attracted great interests from many researchers in recent years. Takagi-Sugeno (T-S) fuzzy model has become a popular and effective approach to control complex systems, and a lot of significant results on stabilization and control via linear matrix inequality (LMI) approach have been reported; see [1–4]. Compared with the centralized control, the decentralized scheme is preferred in the control design issue of the large-scale interconnected systems [5]. Recently, there are some works about stability and stabilization of fuzzy large-scale systems [6–9]. It is well known that delays appear in many dynamic systems, which are potential causes of system instability [10, 11]. The tasks of stabilization and tracking are two typical control problems. In general, tracking problems are more difficult than stabilization problems especially for nonlinear systems [12]. Reference [13] has given decentralized fuzzy model reference tracking control design, and the stable conditions in the sense of Lyapunov are given. The technology of descriptor model transformation is used in [14, 15]. A T-S fuzzy descriptor tracking control design for nonlinear systems with a guaranteed model reference tracking performance is discussed [16]. However, in practical situations, failure of actuators often occurs. Thus, an important requirement is to design a reliable controller such that the stability and performance of the closed-loop system can tolerate actuator failures [17–20]. In this