带泊松跳跃线性随机系统的稳定性与能观测性

发布时间：2018-04-25 13:08

本文选题：泊松跳跃 + 算子谱　；参考：《山东科技大学》2017年硕士论文

【摘要】：带泊松跳跃的随机系统可以更好的描述系统外突然发生的随机扰动,近年来越来越多的学者开始关注这个领域。带泊松跳随机系统在物理、化学、工程、金融、生物系统等领域有着重要应用,研究带泊松跳随机系统有着重要意义。本文主要研究了由泊松跳跃和布朗运动共同驱动的线性随机系统的稳定性与能观测性。主要成果如下:利用谱分析方法得到系统渐近均方稳定的充分必要条件。将“不可移动的谱”的概念推广到带泊松跳线性随机系统的基础上,并得到“不可移动的谱”的判别定理。用“不可移动的谱”为工具给出了系统可否镇定的判别定理。在使用算子谱定义区间稳定的基础上研究了线性随机系统的区间稳定性并得到了系统状态收敛速度与区间(-β,-α)的关系。使用线性矩阵不等式和Schur补引理得到系统区间稳定的判别定理。在定义精确能观测和精确能检测的基础上得到相应的判别定理。在此基础上分析了系统稳定、精确能观测、精确能检测以及广义李雅普诺夫不等式之间的关系。同时,为了方便理解本文在一些章节中给出了数值算例。
[Abstract]:Random systems with Poisson hops can better describe the sudden random disturbance outside the system. In recent years, more and more scholars have begun to pay attention to this field. The stochastic systems with Poisson jump have important applications in the fields of physics, chemistry, engineering, finance, biological systems and other fields. This paper is important to study the random system with Poisson jump. The stability and observability of a linear stochastic system driven by a Poisson jump and Brown motion are studied. The main results are as follows: the necessary and sufficient conditions for the asymptotic mean square stability of the system are obtained by using the spectral analysis method. The discriminant theorem of the mobile spectrum is given by using the "non movable spectrum" as a tool. The interval stability of a linear stochastic system is studied on the basis of the interval stability of the operator spectrum definition, and the relation between the system state convergence rate and the interval (- beta, - alpha) is obtained. Linear matrix inequalities and Sc are used. The HuR complementary lemma obtains the discriminant theorem of system interval stability. On the basis of defining accurate observational and accurate energy detection, the corresponding discriminant theorems are obtained. On this basis, the system stability, accurate energy observation, accurate energy detection and the generalized Lyapunov inequality are analyzed. A numerical example is given in the section.

【学位授予单位】：山东科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211.6

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