部分转移概率信息未知的时滞Markov跳跃系统鲁棒控制研究

Markovian jump systems have been widely used to model various practical systems, such as network system, electric power system and so on. The time delay affecting the stability and performance of the system is unavoidable in these systems. The transition probabilities in the jumping process and initial condition uniquely determine the behavior of Markovian jump systems. At present, the main results on Markovian jump systems are obtained assuming that the information on transition probabilities is completely known, which is not universal. In this project, the problems of robust control for Markovian jump systems with partial information on transition probability and time delay will be investigated. The main contents include three aspects as follows: Firstly, the problem of robust stability for Markovian jump systems with partial information on transition probability and time delay will be investigated. Considering the effects of the defective statistics about the information of transition probability, the improved free-connection weighting matrix method will be proposed. And then the less conservative robust stability criteria will be proposed by using the extended Wirtinger’s inequality. Secondly, the sufficient conditions for designing the robust controller will be derived based on the robust stability criteria. Thirdly, on the basis of the study of robust control method for Markovian jump systems with partial information on transition probability and time delay, the network control method based on Markov model with partial information on transition probability will be discussed. Finally, an efficient and feasible approach for Markovian jump systems with partial information on transition probability is going to be proposed in this project, which has great important theoretical reference for promoting the engineering applications of Markovian jump systems.

Markov跳跃系统在网络系统、电力系统等实际系统中有着广泛的应用，而时滞现象在这些系统中普遍存在，影响着系统的稳定性及性能。转移概率矩阵和初始条件唯一决定Markov跳跃系统的状态轨迹，而目前的研究主要是假设系统的转移概率矩阵完全已知，不具有普遍性。本项目对部分转移概率信息未知的时滞Markov跳跃系统的稳定性和控制器设计展开研究，内容包括：①针对Markov跳跃系统转移概率信息缺失及时滞问题，利用Markov特性分离未知转移概率，结合广义Wirtinger’s不等式，研究具有低保守性的鲁棒稳定性分析方法；②在稳定性分析的基础上，提出系统的鲁棒控制器设计方法；③将所研究的鲁棒控制方法应用到网络控制系统中，探讨基于部分转移概率信息未知Markov模型的网络控制方法。研究结果将为Markov跳跃系统提供一种有效、可行的新方法，对促进Markov跳跃系统的工程实现提供重要的理论参考。

Markov跳跃系统在网络系统、电力系统等实际系统中有着广泛的应用，而时滞现象在这些系统中普遍存在，影响着系统的稳定性及性能。转移概率矩阵和初始条件唯一决定Markov跳跃系统的状态轨迹，鉴于转移概率矩阵信息不完备的情况更符合实际情况，本项目对部分转移概率信息未知的时滞Markov跳跃系统的稳定性和控制器设计展开研究，内容包括： ①针对Markov跳跃系统转移概率信息缺失及时滞问题，考虑到时滞，时滞的上界及它们的差，三者的关系，在广义Wirtinger’s不等式估计Lyapunov函数的弱无穷小算子中的积分项时，不可避免的产生包含时滞信息的分数的情况，创新性的提出伴随分数不等式估计积分项的界，在减少计算复杂度的基础上，提出保守性更低的鲁棒稳定性分析方法；②控制器设计方面，为了减少控制器设计过程中的计算的复杂程度，在稳定性分析的基础上，分别提出了时滞系统模型相关状态反馈控制器的设计方法和事件驱动网络控制系统的输出反馈控制器设计方法；③将所研究的鲁棒控制方法应用到基因调控网络和事件驱动网络控制系统的研究中，针对基因调控系统，提出时滞相关稳定性判据，针对网络控制系统，提出事件驱动网络控制系统的时滞相关稳定性判据和输出反馈控制器设计方法。研究结果为部分转移概率信息未知的时滞Markov跳跃系统提供一种有效、可行的新方法，对促进Markov跳跃系统的工程实现提供重要的理论参考。