Semi-Markovian(SM)随机切换系统是控制学科重要的研究领域，然而由于semi-Markov随机过程的逗留时间依赖特性以及逗留时间本身的随机性，针对其稳定性和控制的定量分析一直是研究难点。本项目以提出SM随机切换系统稳定性分析的充要条件为目标，开展其动态滑模控制策略研究。鉴于semi-Markov随机过程的后效性问题，综合运用逗留时间的分布特性及Markov更新链的概念，建立semi-Markov核模型，提出基于逗留时间和模式依赖的SM随机切换系统稳定性分析的充要条件；在逗留时间和模式依赖Lyapunov函数框架下，针对模型不匹配和切换输入矩阵列不满秩的SM切换系统，提出几类典型的动态滑模控制设计方法；进一步，在各类信息受限情景下，解决复杂SM切换系统的滑模控制问题。本项目的宗旨是建立一套较为完整的SM随机切换系统的分析和滑模控制方法，为其在工程实践中的应用奠定理论基础。

To generalize the scope of stochastic switching systems, a naturally extended research frontier is the semi-Markovian jump systems (S-MJSs) where the transition probabilities will be memory, i.e., the transition probability at each time depends on all the history information of elapsed switching sequences. In realities, many practical systems fall into the scope of S-MJSs, but not MJSs, ranging from various electric circuit systems, multi-legged and omnidirectional mobile robots, biological systems, to communication networks. However, the generality of semi-Markov chain in the capability of modeling stochastic switching leads to considerable complexity in studying the S-MJSs, even the basic stability and stabilization issues. The objectives of this project are to propose a sufficient-and-necessary-stability-analysis framework for S-MJSs, and to develop a dynamic sliding mode control scheme for the nonlinear control-oriented purpose. In particular, for the memory properties of semi-Markov process, fully utilizing the distribution properties of sojourn-time and the definition of Markov updating chain sets up the semi-Markov Kernel model, and is also expected to derive the sufficient and necessary conditions with sojourn-time and mode dependency for the stability analysis of S-MJLSs. Then, based on the sojourn-time and mode-dependent Lyapunov functions, the sojourn-time and mode-dependent sliding mode control design will be carried out, where the purpose is to reduce the design conservatism and improve the dynamic sliding mode performance. For more general S-MJSs with the unmatched model and non-full-column-rank input matrix, the dynamic sliding mode control design procedure will be built. Application of the sliding mode control resulting in complex S-MJSs with parametric uncertainties, state and input delay, input and/or output saturation, and sensor nonlinearity, faults, and limited communication, will be further broached. The underlying theoretical framework will be adapted toward fault diagnosis and tolerant control of robot/sensor network, where the overall dynamics will be modelled via a hierarchy of system models, i.e., S-MJSs, such that the sliding mode control strategy can be based on the high-level model.