【作者】 包俊东；

【导师】 邓飞其；

【作者基本信息】 华南理工大学 ， 控制理论与控制工程， 2004， 博士

【摘要】 本学位论文基于Lyapunov稳定性理论，利用It(?)公式、随机分析原理、Grownwall-Bellman不等式、Schur余(补)、矩阵不等式等工具和、Lyapunov-Krasovskii泛函(函数)等方法，研究了随机时滞系统、主要对象是一般性分布型时滞系统的鲁棒稳定性和鲁棒控制器的设计问题，特别是对具有Markov跳变参数的分布型时滞系统稳定性及镇定问题的判定条件做了深入的研究，建立了一些有效的判据，获得了若干有意义的成果。 本学位论文的主要工作有以下几个方面： 第一，讨论了一类具有不确定参数的随机控制系统的指数稳定性。证明了标称系统的最优控制器可以保证系统的鲁棒镇定。得出了最优控制器关于结构不确定性的鲁棒性质。给出了系统的均方指数镇定的代数判据。 第二，考虑了具有马尔可夫跳变参数以及带有不确定性参数系统的鲁棒稳定性。利用随机系统的代数Riccati方程(SARE)，以及相应的最优控制律。基于上述事实，分析了最优调节器的鲁棒性。得出了标称系统的最优控制器关于跳变参数以及关于结构不确定性所具有的鲁棒性能。基本上保持了对成本权重矩阵不定的要求，并给以数值例子加以说明结论的正确性。 第三，研究了一类具有多时滞、以及马尔可夫跳变参数的随机微分系统和具有分布型时滞的马尔可夫跳变参数及白噪声的微分系统。主要考虑随机系统的二次最优控制(SLQ)问题的最优控制器关于不确定性、时滞及马尔可夫跳变参数的鲁棒镇定问题。分析了系统的均方指数稳定性。并建立了时滞相关与时滞无关的代数判据。得出了标称系统的最优控制器关于时滞因素以及马尔可夫跳变参数所带来的干扰的鲁棒性。得到了保守性相对小的，时滞相关的充分条件。 第四，考虑了传统意义下的线性二次型(LQ)最优控制问题对于结构不确定性、时滞、随机干扰等因素的鲁棒性能。考察了一类拟线性具有不确定性参数结构、Markov跳变参数及时滞干扰的随机微分系统的鲁棒指数镇定问题。利用最优控制规律其自身的特点，比如Riccati方程等，给出了标称系统的最优控制器所具有的鲁棒性能，可以镇定相应的具有时滞的和不具有时滞以及不确定性随机系统的结论。即，标称系统的最优调节器可以保证系统的鲁棒稳定性。 对于线性二次最优控制器的鲁棒可镇定问题，本文做了较为深入、详细的研究。添补了这方面的研究空白。 第五，介绍了不确定性线性分布型时滞随机系统的鲁棒指数稳定性问题。主要考虑了更为一般形式的分布型时滞系统。采用Lyapunov-Krasovskii泛函、Schur余与线性矩阵不等式(LMIs)相结合的方法。考虑该类系统的均方指数稳定性的充分条件。得到了时滞无关，时滞相关的均方指数稳定性的LMI判据。更多还原

【Abstract】 In this dissertation, based on the Lyapunov stability theory, Ito formula, the principle of stochastic analysis, and the tools of Grownwall-Bellman inequality, Schur Complement, matrix inequalities, Lyapunov-Krasovskii functional (function) etc. are employed to study stochastic delay systems. Mainly, the systems with comprehensive type of distributed delay are concerned about, the problems of robust stability and the design of robust controllers are considered. Especially, stability and stabilization of distributed delay systems with Markovian jumping parameters is deeply studied. Some efficiency criteria are established. Significant results are obtained.The main contributions of this dissertation are as follows:In the first, Exponential stability of a class of stochastic control systems with uncertain parameters is discussed. The fact that the optimal controller of nominal system can guarantee the robust stabilization of the systems is shown. The robustness of the optimal controller for uncertain parameters of systems and the algebraic criteria of exponential stability in mean square are obtained.Second, robust stability of systems with Markovian jumping parameters and with uncertainties is considered. The stochastic algebraic Riccati equation and corresponding optimal controller are employed. Based on the above factors, the robustness of the optimal regulator is analyzed. The robust performance of the optimal controller of nominal system about the disturbance of Markovian jump parameters and structural uncertainties is obtained. The un-definiteness of weight matrix is maintained. Numerical example is illustrated to show the correctness of the results.In the third, a class of stochastic differential systems with Markovian jumping parameters and white noise as well as distributed delay is studied. The robust stabilization of the optimal controller that is derived by stochastic linear quadratic optimal control problem about the uncertainties and the jumping parameters is considered mostly. Exponential stability in mean square of the systems is analyzed. The delay independent and delay dependent algebraic criteria are established. The robustness of optimal controller for the disturbance of the delay and Markovian jumping parameters is shown. The delay dependent, less conservative, sufficient condition is obtained.Fourth, the traditional linear quadratic (LQ) optimal control problem has been更多还原