马尔科夫跳跃中立型系统的分析与设计

本项目基于控制理论基础，以已知的和不确定的传输概率为实际背景，拟用Lyapunov稳定性理论及相关分析技巧，系统地开展对马尔科夫跳跃中立型系统的暂态性和稳态性的分析与设计的研究,达到改进现有研究结果的保守性和充实中立型动力系统的研究内容的目的。 项目主要研究内容包括：研究Wirtinger等新不等式的性质提出新的离散Lyapunov泛函方法；构造新的 Lyapunov 泛函结合不等式分析技巧等方法研究各类型系统得到保守性较低的时滞依赖矩镇定性条件；结合马尔科夫跳跃特性和常数变易思想探讨马尔科夫跳跃中立型系统的几乎必然镇定性条件；利用能量函数、模型依赖平均驻留时间、无源性控制等方法分析马尔科夫跳跃中立型系统的异步切换控制和无源性准则问题，并设计在不同情形下的控制器。 通过本项目的研究，期望能够完善中立型动力系统的理论体系，拓展中立型系统的应用领域，推动混杂动力学系统的分析与研究。

This project is based on the basic knowledge of control theory, setting known and unknown transmission probability as actual background, using Lyapunov stability theories and relevant analyzing skills, we can reach the goal of improving the conservatism of the existing results as well as enrich and complete the researching contents of neutral dynamical system by doing some study about analyzing and designing of the transient and the steady-state nature of Markov jump neutral system in a systematic way. The major studying contents of the project including the followings, studying new methods of discrete Lyapunov functional approach based on the nature of the Wirtinger and other inequations, studying the less conservative delay-dependent moment stabilization for different kinds of Markovian jump system by constructing new Lyapunov functional combination of inequations analysis techniques, discussing almost sure stabilization of Markov jump neutral system by combining the thoughts of Markov jump characteristics and the method of variation of constant and so on. Analyzing the problem of asychronous switching and passivity control, and designing controllers for Markov jump neutral system which can be efficient in different situations by using the methods of energy functions, model-dependent average dwell time, passive control and so on. After the study of this project, we are expecting to promote the theoretical system of neutral dynamical system, as well as to enrich practical field of neutral systems and to enhance the analysis and research of hybrid dynamical system.