时滞奇异随机跳变系统容许性分析与控制器设计研究

Singular stochastic jump systems are a class of important dynamic systems with extensive forms. Singular stochastic jump systems appear in many fields, such as power systems, electrical networks, social economic systems, and so on.. This project is concerned with the problems of admissibility analysis and controller design for several kinds of singular stochastic jump systems with time delays. The main aim of this project is to get and develop effective methods so as to thoroughly investigate admissibility and controller designing issues of the mentioned singular stochastic systems . It is of great significance to implement the project not only from the view of theory research but also from practical applications. Some problems in the project are still open, which will be difficult and full of challenges. . The main contents of the project are as follows: .(1) By designing state and output feedback controllers, the stability and normalization problems for singular Markovian jump systems with retarded or neutral delays will be concerned;.(2) Suppose the parameters matrices such as Ei have perturbations, the aforesaid problems of the stability and normalization problems for singular Markovian jump systems with retarded or neutral delays will be considered; .(3) Considering the stochastic disturbance, the problems of admissibility and controller design for Itô stochastic singular Markovian jump systems with retarded or neutral delays will be studied based on L-K functional analysis; .(4) Applying Lasalle-type theorems and Barbalat lemmas, the above problems of admissibility and controller design for Itô stochastic singular Markovian jump systems with retarded or neutral delays will be investigated.. The project will supply novel and effective control methods for the practical applications of singular stochastic systems, establish a set of complete theoretical framework, push forward the enrichment and development of control theory and practical applications of singular stochastic systems actively.

奇异随机跳变系统是一类具有广泛形式的动力系统，能有效地描述电力系统、电路系统、社会经济系统等实际系统。本课题将以时滞奇异随机跳变系统为研究对象，旨在提出有效的容许性分析与控制器设计方法。无论从理论分析上还是工程实践上都具有较大的现实意义, 而且研究难度较大,很多问题都是开放性的，极富挑战性。.首先设计反馈控制器来研究迟钝型、中立型时滞奇异跳变系统及其参数矩阵Ei等发生摄动时的正常化问题和稳定性分析。然后，应用Lyapunov-Krasovskii泛函分析法来研究Itô型随机时滞奇异跳变系统的容许性和控制器设计问题。最后，应用Lasalle型定理法及Barbalat引理法来研究Itô型随机时滞奇异跳变系统的容许性和控制器设计问题。.本项目将为奇异随机系统在实际中的应用提供新的研究方法和切实有效的控制途径,以期对奇异随机系统控制理论的丰富和发展及其在工程实践中的应用起到积极的推动作用。

奇异随机跳变系统是一类具有广泛形式的动力系统，能有效地描述电力系统、电路系统、社会经济系统等实际系统。本项目以时滞奇异随机跳变系统为研究对象，提出了有效的容许性分析与控制器设计方法。无论从理论分析上还是工程实践上都具有较大的现实意义，而且研究难度较大，很多问题都是开放性的，极富挑战性。. 本项目设计反馈控制器研究了迟钝型、中立型时滞奇异跳变系统及其参数矩阵Ei等发生摄动时的正常化问题和稳定性分析。应用Lyapunov-Krasovskii泛函分析法研究了Itô型随机时滞奇异跳变系统的容许性和控制器设计问题。应用Lasalle型定理法及Barbalat引理法研究了Itô型随机时滞奇异跳变系统的容许性和控制器设计问题。. 本项目为奇异随机系统在实际中的应用提供了新的研究方法和切实有效的控制途径，对奇异随机系统控制理论的丰富和发展及其在工程实践中的应用起到了积极的推动作用。