【作者】 陈云；

【导师】 薛安克；

【作者基本信息】 浙江大学 ， 控制科学与工程， 2008， 博士

【摘要】 许多实际动态系统中存在大量的非确定性（即随机）现象。对于这样的系统,无法用常微分方程表示,而需借助随机微分方程。另外,网络控制、生产过程控制、人口及经济等系统存在时间滞后现象,即系统的现状及发展趋势与系统过去的状态相关。近年来,基于随机时滞微分方程描述的随机时滞系统的研究是控制理论界的一个研究热点。本文利用Lyapunov-Krasovskii泛函方法,以线性矩阵不等式（LMI）为工具,研究随机时滞系统的分析与综合问题。主要包括以下内容:1.利用积分不等式方法研究determinisitc时滞系统的指数稳定性问题。证明所得结果与文献中结果的等价性,但是本文结果由于具有更少的LMI维数和变量个数而更加简单。在分析时滞系统研究现状的基础上,提出了利用积分不等式研究随机时滞系统的方法。通过引入一个附加的向量得到随机意义下的积分不等式。利用该积分不等式和自由加权矩阵方法,建立随机时滞系统的时滞相关方法。利用该方法研究随机时滞系统的时滞相关指数均方稳定性。该方法可以避免模型变换和交叉项的界定。在处理满足Lipchitz线性增长条件的非线性扰动时,利用向量和矩阵的秩性质,避免使用现有方法中的矩阵不等式约束条件,从而降低结果的保守性。2.利用积分不等式方法研究随机时滞系统的时滞相关鲁棒镇定、鲁棒H_∞控制和基于观测器的输出反馈控制问题。若随机扰动不存在,本文的有界实引理（BRL）将与文献中deterministic时滞结果等价,但本文结果具有更简单的形式。利用奇异值分解（SVD）方法,将基于观测器的输出反馈控制器存在条件用严格线性矩阵不等式（LMI）表示。3.利用积分不等式方法研究随机时滞系统的时滞相关随机无源性问题。将deterministic系统的无源性定义进行拓展,给出It（?）随机时滞系统随机无源的定义。建立随机时滞系统时滞相关的随机无源性条件,并设计随机无源控制器。4.利用积分不等式方法讨论随机时滞系统的时滞相关L₂—L_∞和H_∞滤波问题。所得的L₂—L_∞性能分析结果与文献中利用自由加权矩阵方法得到的结果是等价的,但本文结果具有更简单的形式。5.利用积分不等式方法,研究具有Markovian跳变参数的随机时滞系统时滞相关稳定性分析和H_∞性能问题,以及随机时滞神经网络的时滞相关稳定性分析和状态估计问题。最后,对全文进行概括性总结,并提出了今后需要继续研究的方向。更多还原

【Abstract】 The nondeterministic （i.e. stochastic） phenomena are frequently encountered in many practical systems. These systems should be described by stochastic differential equations instead of ordinary differential ones. On the other hand, time delays are included in many practical systems, such as networks control systems, production process control systems, population and economic dynamic systems and so on, i.e. the current and future states of the systems dependent on their departed states. In recent years, the study of analysis and synthesis of stochastic time-delay systems, which are described by stochastic delayed differential equations, is a popular topic in the field of control theory.This thesis focuses on analysis and synthesis of stochastic time-delay systems based on Lyapunov-Krasovskii theory and LMI approach. The main works of this thesis are as follows:1. Based on an integral inequality, the exponential stability of deterministic time-delay systems is investigated. It is proved that the obtained result is equivalent to certain existing one. But our result is simpler, since it has less dimensions of LMI and less number of variables. By analyzing the main results of systems with time delays, the integral inequality method is proposed to investigates stochastic delayed systems. By introducing an additional vector, an integral inequality in stochastic context is derived. Based on this inequality and free-weighting matrix technique, delay-dependent method for stochastic delayed systems is established. This new method is employed to discuss exponential mean-square stability of stochastic systems with delays, which avoids model transformations and bounding techniques for cross terms. While dealing with the nonlinear perturbation which satisfies Lipchitz linear growth condition, the matrix inequality condition in existing reports is removed by using the trace characteristic of vector and matrix, such that the result is less conservative.2. Based on integral inequality approach, the problems of delay-dependent ro- bust stabilization, robust H_∞control and observer-based output feedback control for stochastic delay systems are considered. If there is no stochastic perturbation, the bounded real lemma （BRL） is equivalent to some existing ones in deterministic setting but with simpler forms. Based on singular value decomposition （SVD） approach, the condition for the existence of observer-based output feedback controller is formulated in terms of strict LMIs.3. The stochastic passivity of stochastic time-delay systems is investigated by using integral inequality method. The stochastic passivity of stochastic systems is defined by extending the deterministic ones. Delay-dependent passivity condition and control for stochastic delayed systems are presented.4. The issues of delay-dependent L₂- L_∞and H_∞filtering for stochastic time-delay systems are handled by applying the integral inequality method. The presented L₂-L_∞performance result is equivalent to some existing one, which is obtained by using free-weighting matrix technique, but our result is simpler.5. By integral inequality approach, delay-dependent stability and H_∞performance analysis for stochastic delayed systems with Markovian jumping parameters are discussed. In addition, delay-dependent stability and state estimation for stochastic delayed neural networks are considered.Finally, the concluding remarks are summarized, and the future research studies are pointed out.更多还原