Theory Of T-S Fuzzy Systems And Its Application In Control

There exist a large number of non-linear, delay and uncertainty phenomena in nature and human societies. Because of being able to approximate any smooty nonlinear function to any specified accuracy with any compact set, Takagi-Sugeno (T-S) fuzzy model with time delay, as a portrait of the mathematical model of these phenomena, are worthy of our theoretical research and applied research. State estimator (filtering) is to estimate the unknown state in system via measurable observed signal, which is one of basic problems in the area of control and signal processing. Kalman filtering approach is limited to its applications because that it requires the exact knowledge of the statistics of the external noise signals. Since that it does not require the exact statistics and it is insensitive to the uncertainties both in the exogenous signal statistics and in dynamic models, the Hoo filtering approach has attracted more and more attention in the past decade, and serval efforts also have been made on this issue. This dissertation makes a thorough study for the problem of stability analysis and (non-fragile) robust H∞filtering of uncertain system and T-S fuzzy systems with time-varying delays by using the Lyapunov stability theory and Hoo filtering theory, and by making full use of convex optimization approach and linear matrix inequality (LMI) techniques. The main results are as follows:(1) The problems of robust stability analysis of uncertain T-S fuzzy systems with interval time-varying delays are studied. The system uncertainty is assumed to be time-varying and norm-bounded. Exploiting the delay-partitioning approach and delay-depedent Lyapunov-Krasovskii functional (LKF) method, respectively, we construct some novel LKFs and make full use of the information of time delays and cross terms in these LKFs when estimating the upper bound of these derivatives. These proposed results are some less conservative delay-derivative-dependent stability conditions, which are obtained in terms of linear matrix inequalities. These conditions are derived that depend on both the upper and lower bounds of the delay derivatives. Finally, some numerical examples are given to demonstrate the merit and reduced conservatism of these proposed results.(2) The problem of robust Hoo filter design for uncertain systems with time-varying state and distributed delays is investigated. These delays are assumed to be time-varying delays being differentiable uniformly bounded with delay-derivative bounded by a constant, which may be greater than one. A novel delay-partition-type LKF is constructed, and a tighter upper bound of its derivative is obtained by making full use of improved matrix inequality technique, then the proposed result has advantages over some existing results, in that it has less conservatism and it enlarges the application scope. A new delay-derivative-dependent approach of robust Hoo filter design for the uncertain system is proposed. Finally, illustrative examples are given to show the effectiveness and reduced conservatism of the proposed approach.(3) The Hoo filter design problem is investigated for T-S fuzzy systems with interval time-varying delay. First, since we construct a novel LKF which contains the information of the time-varying delay and consider fully these useful terms and some adverse magnifications, a delay-derivative-dependent Bound Real Lemma (BRL) condition is deduced and has advantages over some previous results in that it enlarges the application scope but has less conservatism, which is established theoretically. Second, based on the above BRL condition, a new H∞filter scheme is proposed. At last, some numerical examples and an application to the truck-trailer system are utilized to demonstrate the merit and reduced conservatism of the proposed approach.(4) Against with those works on the Hoo filtering problem are based on an implicit assumption that the filter would be designed and implemented exactly. The problem of non-fragile robust Hoo filtering for uncertain T-S fuzzy systems with interval time-varying delays is studied. Our objective is to design a robust Hoo filter such that the filtering error system is asymptotically stable with a prescribed Hoo performance, where the filter to be designed is assumed to have some gain perturbations. The system uncertainty is assumed to be norm-bounded time-varying parametric uncertainty. First, a noval LKF is also constructed by fully considering the relation of the terms in the LKF and a tighter upper bound of its derivative is estimated by using improved Jensen’s Inequality technique, and an improved Bound Real Lemma (BRL) condition is obtained. Second, based on the above BRL condition, a new non-fragile robust Hoo filter scheme is proposed. Finally, some numerical examples are utilized to demonstrate the effectiveness and reduced conservatism of the proposed scheme.