摘要
首先，本文针对不确定Takagi-Sugeno(T-S)模糊中立型系统，分别研究了其鲁棒非脆弱H_∞控制问题、鲁棒H_∞滤波设计问题、保成本可靠控制问题和鲁棒H_∞DOF(动态输出反馈)控制问题；其次，本文研究了一类随机脉冲泛函微分方程的稳定性以及一类随机脉冲T-S模糊时滞系统的状态反馈模糊控制问题．全文共八章，主要研究内容分为六个部分：
第一部分针对一类具有线性分式不确定的T-S模糊中立型系统的鲁棒非脆弱H_∞控制问题进行了研究．利用Lyapunov-Krasovskii泛函、线性矩阵不等式(LMI)方法和描述系统方法(Descriptor System Approach)，提出了使闭环系统渐近稳定并且满足H_∞性能的非脆弱H_∞控制器设计方法．
第二部分针对一类具有时变时滞的不确定T-S模糊中立型系统的鲁棒H_∞滤波设计问题进行了研究．通过Lyapunov-Krasovskii泛函、Barbalat引理和LMI方法，提出了使误差滤波系统渐近稳定并满足H_∞性能的全阶滤波器设计方法．此外，作为理论的应用，还讨论了一类非线性中立型系统—长线隧道二极管分布式网络的H_∞滤波问题．
第三部分针对一类不确定T-S模糊中立型系统的保成本可靠控制问题进行了研究．考虑到实际控制系统中执行器非理想化的事实，利用连续故障模型引入更接近实际的系统模型．通过Lyapunov-Krasovskii泛函、描述系统方法、自由权矩阵方法(Free Weighting Matrix Method)和LMI方法，提出了具有二次成本函数约束的保成本可靠控制器的设计方法．此外，通过“mincx”优化算法得到了成本函数的极小化上界．
第四部分针对一类不确定T-S模糊中立型系统的鲁棒H_∞DOF控制问题进行了研究．通过Lyapunov-Krasoviskii泛函、Barbalat引理和LMI方法，提出了使闭环系统鲁棒渐近稳定并满足H_∞性能指标的全阶DOF控制器设计方法．
第五部分针对一类随机脉冲泛函微分方程的稳定性进行了研究．利用Lyapunov-Krasovskii泛函、It(?)公式以及数学分析技巧，提出了随机脉冲泛函微分方程均方稳定的新判据．最后，作为理论的应用还讨论了一类随机脉冲时滞神经网络的均方稳定性．
第六部分针对一类随机脉冲T-S模糊时滞系统的反馈控制设计问题进行了研究，其中时滞不但出现在系统状态变量中，而且还出现在控制输入变量中．利用It(?)公式、Lyapunov-Krasovskii泛函以及松弛线性矩阵不等式(Relaxed LMI)方法，以LMIs的形式提出了使闭环系统均方指数稳定的状态反馈模糊控制器设计方法．
论文的结束部分对全文所做的工作进行了总结，并指出了下一步研究的方向．
Firstly, this doctoral dissertation studies, respectively, the problems of robust nonfragileH_∞control, robust H_∞filtering, robust reliable guaranteed cost control and robustH_∞dynamic out-put feedback(DOF) control for Takagi-Sugeno(T-S) fuzzy neutralsystems. Secondly, the stability analysis for a class of impulsive stochastic delayed differentialequations and the problem of state-feedback fuzzy control for a class of impulsivestochastic T-S fuzzy delayed systems are investigated, respectively. The dissertation consistsof six parts with eight chapters:
Part 1 contributes to the problem of robust non-fragile H_∞control for a class ofuncertain T-S fuzzy neutral systems with linear fractional parametric uncertainties. Bymeans of Lyapunov-Krasovskii functional, the LMI approach and descriptor system approach,the design solution of robust non-fragile H_∞controller is obtained, which ensuresasymptotic stability of the closed-loop system and guarantees a prescribed H_∞performancelevel.
Part 2 is to study the problem of robust H_∞filtering for a class of uncertain T-Sfuzzy neutral systems with time-varying delays. On the basis of Lyapunov-Krasovskiifunctional, Barbalat lemma and the LMI approach, a full-order fuzzy H_∞filter is obtained,which ensures asymptotic stability of the filtering error system and guarantees aprescribed H_∞performance level. Moreover, as an application of the theoretical results,the H_∞filter design problem for a neutral-type nonlinear distributed network (long linewith tunnel diod) is discussed.
Part 3 is devoted to investigating the problem of robust reliable guaranteed cost controlfor a class of uncertain T-S fuzzy neutral systems. Based on the fact that actuatorsare non-ideal in real control systems, a more practical system model is introduced byuse of the continuous fault model. The design solution of robust reliable guaranteed costcontroller with constraint of quadratic cost function is obtained via Lyapunov-Krasovskiifunctional, the descriptor system approach, the free weighting matrix method and LMIapproach. Furthermore, the minimum upper bound of the cost function can be derived viathe "mincx" optimal algorithm.
Part 4 focuses on the problem of robust H_∞dynamic output-feedback (DOF) control for a class of uncertain T-S fuzzy neutral systems. Utilizing Lyapunov-Krasoviskii functional,Barbalat lemma and the LMI approach, a full-order fuzzy DOF controller has beendevised, which ensures the asymptotic stability of the closed-loop system and guaranteesa prescribed H_∞performance level.
Part 5 is concerned with the stability analysis for a class of impulsive stochasticdifferential equations with delays. By means of Lyapunov-Krasovskii functional, It(?) formulaand mathematical analysis, new sufficient conditions ensuring mean square stabilityof the impulsive stochastic functional differential equations are obtained. Finally, as anapplication of the theoretical results, the mean square stability of a class of stochastic impulsiveneural networks with delays is discussed.
Part 6 investigates the problem of state-feedback fuzzy control for a class of stochasticT-S fuzzy delayed systems with impulsive effects. The time delay is assumed to appearboth in the state and control input. On the base of It(?) formula, Lyapunov-Krasovskiifunctional and the relaxed linear matrix inequality (Relaxed LMI) approach, the designsolution of state-feedback fuzzy controller is proposed in terms of LMIs such that theresulting closed-loop system is exponentially stable in the mean square.
At the end of this dissertation, the results are summarized and further research problemsare pointed out.
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