Sliding Mode Control for a Class of Multiple Time-Delay Systems

Time-delay frequently occurs in many practical systems, such as chemical processes, manufacturing systems, long transmission lines, telecommunication and economic systems, etc. Since time-delay is a main source of instability and poor performance, the control problem of time-delay systems has received considerable attentions in literature, such as [1][9]. The design approaches adopt in these literatures can be divided into the delaydependent method [1]-[5] and the delay-independent method [6]-[9]. The delay-dependent method needs an exactly known delay, but the delay-independent method does not. In other words, the delay-independent method is more suitable for practical applications. Nevertheless, most literatures focus on linear time-delay systems due to the fact that the stability analysis developed in the two methods is usually based on linear matrix inequality techniques [10]. To deal with nonlinear time-delay systems, the Takagi-Sugeno (TS) fuzzy model-based approaches [11]-[12] extend the results of controlling linear time-delay systems to more general cases. In addition, some sliding-mode control (SMC) schemes have been applied to uncertain nonlinear time-delay systems in [13]-[15]. However, these SMC schemes still exist some limits as follows: i) specific form of the dynamical model and uncertainties [13]-[14]; ii) an exactly known delay time [15]; and iii) a complex gain design [13]-[15]. From the above, we are motivated to further improve SMC for nonlinear timedelay systems in the presence of matched and unmatched uncertainties. The fuzzy control and the neural network control have attractive features to keep the systems insensitive to the uncertainties, such that these two methods are usually used as a tool in control engineering. In the fuzzy control, the TS fuzzy model [16]-[18] provides an efficient and effective way to represent uncertain nonlinear systems and renders to some straightforward research based on linear control theory [11]-[12], [16]. On the other hand, the neural network has good capabilities in function approximation which is an indirect compensation of uncertainties. Recently, many fuzzy neural network (FNN) articles are proposed by combining the fuzzy concept and the configuration of neural network, e.g., [19]-[23]. There, the fuzzy logic system is constructed from a collection of fuzzy If-Then rules while the training algorithm adjusts adaptable parameters. Nevertheless, few results using FNN are proposed for time-delay nonlinear systems due to a large computational load and a vast amount of feedback data, for example, see [22]-[23]. Moreover, the training algorithm is difficultly found for time-delay systems.