| Nonlinearity and time delay can be found in various engineering systems, which are hotspots and difficulties in area of control. Takagi-Sugeno (T-S) model combining the traditional control theories with expert knowledge has become the important method of dealing with complex nonlinear systems and received more and more attention. So, it is of great theoretical and practical significance that research on the T-S fuzzy time-delay systems.Based on Lyapunov functional method, by using linear matrix inequality (LMI), this dissertation studies the problems of delay-dependent H∞control, H∞filtering, L2-L∞filtering for uncertain T-S fuzzy time-varying delay system and uncertain stochastic T-S fuzzy time-varying delay system. The main work and contribution of this dissertation are listed as follows.1. The delay-dependent robust stability problem of uncertain continue (discrete) T-S fuzzy time-varying delay system is studied, based on this study, we researched the H∞problem for the uncertain continue (discrete) T-S fuzzy time-varying delay systems.Based on the former research, we propose a new Basis-dependent Lyapunov-Krasovskii functional. Then, we present a delay-dependent state feed- back robust H∞controller in term of LMIs, this controller guarantees the continue uncertain T-S fuzzy time-varying delay system not only asymptotically stable but also a prescribed H∞attenuation level. Compared with the current literatures, this controller is much less conservative. At the same time, we extend this Lyapunov-Krasovskii functional method to discrete uncertain T-S fuzzy time-varying delay system, and also obtain a design scheme of delay-dependent robust H∞controller with less conservatism in term of LMIs2. Delay-dependent robust H∞filtering and L2-L∞filtering problems of uncertain continue T-S fuzzy time-varying delay systems are studied.Based on the results of H∞control for uncertain continue T-S fuzzy time- varying delay system, we propose a delay-dependent criterion in term of LMIs, which guarantees a prescribed H∞attenuation levelγfor the filtering error system. Then, a delay-dependent robust H∞filter with less conservatism is proposed in LMIs. The corresponding robust L2-L∞filter is given by using the same method.3. Delay-dependent robust H∞control problem of uncertain stochastic continue T-S fuzzy time-varying delay system is studied.First, based on the new Basis-dependent Lyapunov-Krasovskii functional, we propose a sufficient criterion in term of LMIs such that the closed-loop uncertain stochastic continue T-S fuzzy time-varying delay system is asymptotically stable in mean square and a prescribed H∞performance in mean square is achieved. Then based on this sufficient condition, the robust H∞controller with less conservatism is presented in term of LMIs.4. Delay-dependent robust H∞filtering and L2-L∞filtering problems of uncertain stochastic continue T-S fuzzy time-varying delay systems are studied.Based on the results of H∞control for uncertain stochastic continue T-S fuzzy time-varying delay system, we propose a delay-dependent criterion in term of LMIs, which guarantees a prescribed H∞attenuation levelγin mean square for the filtering error system. Then, a delay-dependent robust H∞filter is proposed in LMIs. The corresponding robust L2-L∞filter is given by using the same method.5. Finally, applying the results of uncertain continue T-S fuzzy time-varying delay system proposed in this dissertation, we study the backing-up control of truck-trailer with bounded energy disturbance.We model a uncertain continue T-S fuzzy time-varying delay model for the truck-trailer system with energy-bounded disturbance and state delay, then, we propose a robust H∞controller in term of LMIs, which guarantees the truck-trailer system a prescribed H∞performance. Simulation demonstrates the effectiveness of the fuzzy controller design scheme we proposed.
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