Robust Sampled-Data Control Design of Uncertain Fuzzy Systems with Discrete and Distributed Delays

Abstract

Nonlinear time-delay systems appear in many engineering systems and system formulations such as transportation systems, networked control systems, telecommunication systems, chemical processing systems, and power systems. Hence, it is important to analyze and synthesize such time-delay systems. Considerable research on nonlinear time-delay systems has been made via fuzzy system approach in (2), (6), (9), (12), (13) where stability conditions of fuzzy systems with discrete delays have been given in terms of Linear Matrix Inequalities (LMIs). Takagi-Sugeno fuzzy systems, described by a set of if-then rules which gives local linear models of an underlying system, represent a wide class of nonlinear systems. In the last two decade, Takagi-Sugeno fuzzy system has been extensively used for nonlinear control systems since it can universally approximate or exactly describe general nonlinear systems((8)). Theory has been extended to fuzzy systems with distributed delays in (7), (11), (15). Those results are based on continuous-time delay systems. From a practical point of view, sampled-data control is of importance. However, only a few results on sampled-data control for fuzzy system with discrete delays have been given in the literature ((1), (5), (14), (16)). Sampled-data controller design has been made for fuzzy systems with distributed delays in (3) and (4). To the best of our knowledge, no result for fuzzy sampled-data control systems with neutral and distributed delays has appeared yet. In this paper, we propose a design method for robust sampled-data control of uncertain fuzzy systems with discrete, neutral and distributed delays. A zero-order sampled-data control can be regarded as a delayed control. Hence, a time-varying delay system approach is taken to design a sampled-data controller. We first obtain a stability condition by introducing an appropriate Lyapunov-Krasovskii functional with free weighting matrices, which reduce the conservatism in our stability condition. Then, based on such an LMI condition, we propose a robust sampled-data control design method of fuzzy uncertain systems with discrete, neutral and distributed delays. We also propose a sampled-data observer design method of fuzzy time-delay systems. A similar approach is taken for analysis of a sampled-data observer, and a condition for an existence of an observer is given by another LMI, which is a dual result of stabilizing controller. Finally, we give some illustrative examples to show our design procedures for sampled-data controller and observer. 23