【作者】 姚素娜；

【导师】 张维海；

【作者基本信息】 山东轻工业学院 ， 检测技术与自动化装置， 2008， 硕士

【摘要】 随机系统可稳性问题的研究是解决许多随机问题的前提需要,一些学者对随机系统稳定性及可稳性进行了研究,其中包括Lyapunov函数法和谱算子分析法。本文基于线性矩阵不等式和随机谱理论,研究了离散系统具有区域极点配置的H₂ /H_∞滤波问题、随机系统谱算子的带状区域（-β,-α）极点配置问题（类似于确定性系统的极点配置概念）、具有谱约束的随机系统H_∞滤波问题以及具有带状谱区域约束的H₂ /H_∞控制问题。本学位论文共分以下几部分:本文首先阐述了随机系统稳定性和谱理论的研究现状与研究意义,介绍了本学位论文的研究的思想方法与和整体结构。为了论文内容的完整性,简单给出了线性矩阵不等式、随机渐进均方稳定性、H_∞滤波和混合H₂ /H_∞滤波以及谱算子理论等若干概念。其次,针对离散系统,通过H₂范数和H_∞范数考虑H₂和H_∞性能指标约束,并结合区域极点配置要求,应用线性矩阵不等式凸优化方法将多目标H₂ /H_∞滤波问题转化为单一目标的优化问题。不仅解决了离散系统具有区域约束的滤波问题,而且区域的极点配置范围得到改善。然后,重新定义了随机系统谱算子,找到了随机系统既满足α域稳定,又满足H_∞性能指标的充分条件,并且给出了带有独立噪声的随机系统滤波器的设计方法。本文最后研究了在满足一定外部扰动抑制水平的情况下,随机系统在谱的带状区域随机均方稳定的充分必要条件。更多还原

【Abstract】 The study of stochastic stability has become premise need of many basic stochastic problems. Many scholars have studied stochastic stability and stabilizability. The one of the most important researches is stochastic spectrum theory, which was developed in [7].Based on LMI and stochastic spectrum theory, we study the discrete H₂ /H_∞filtering problem with regional pole assignment, pole assignment problems with strip region from -βto -αof stochastic system spectrum operator and stochastic system H_∞filtering problems with spectrum constraint as well as H₂/ H_∞control- ler design with strip region spectrum constraint. This artical is divided as following several parts:In chapter one,we present situation and research significance of stochastic system stability,the spectrum theory and introduce the global architecture and research method. In order to integrity the paper content,we give out some definitions such as linear matrix inequality,stochastic asymptotic square stability H_∞filtering,mixed H₂ /H_∞filtering and spectrum operater theory.Chapters three to five are main parts of our paper.The constraint of H₂ and H_∞index of discrete systems is combined with regional pole assignment,we convert multiple object filtering problems to sole goal optimized question by means of LMIs.We solve the filtering problems of discrete systems with regional constraint and the pole assignment scope is improved. Chapter four redefines spectrum operater and finds the full essential condition which satisfiesαregion stable and H_∞performa- nce index. We also give out the filter’s designing method of stochastic systems with dependent noise. In chapter five,we research the full essential condition of stochastic square stability under spectrum’s strip region and certain external constraint levels.Chapter six has made a conclusion and forecast to the whole article.We conclude the main contribution,and some problems have been stated for further study.更多还原