Semi-Markovian(SM)跳跃系统作为一类服从semi-Markov过程/链的多模态随机切换系统，其对很多随机特性以及混杂系统具有强大的建模能力。由于SM跳跃系统的时变转移概率特性和时滞现象的普遍存在，使得这类随机系统的分析和综合仍面临着许多挑战。针对上述关键问题，本项目首先基于新型逗留时间依赖SM Lyapunov函数，研究SM跳跃系统的广义耗散性能分析、各类输出反馈控制器设计以及状态估计问题，然后基于输入-输出方法，研究时滞SM跳跃系统的有记忆控制和滤波问题。在此基础上，进一步研究在系统参数不确定、控制器和传感器饱和、失效等各类信息受限情景下复杂SM跳跃系统的分析和综合问题。此外，本项目的部分理论研究成果将在燃气轮机故障诊断及容错控制系统中进行尝试性应用研究。本项目的宗旨是提出一套较为完整的SM跳跃系统的分析、控制综合以及状态估计方法，为SM跳跃系统在实际应用中提供理论支持。

Differing from the nondeterministic switching in switched systems, the modes evolution in semi-Markovian jump systems (S-MJSs) is determined by a semi-Markov process or chain. It is known that S-MJSs find many applications in industrial processes, which are subject to abrupt variations in their structures and parameters, due to random failures or repairs of components, changing subsystem interconnections, sudden environmental disturbances, etc. However, the properties of time-varying transition probabilities and time-delays exist commonly in S-MJSs, which lead to the analysis and synthesis of S-MJSs rather cutting-edge and challenging. In response to these problems, based on a novel sojourn-time-dependent semi-Markovian Lyapunov function, the stability analysis, output feedback controller design and state estimation for a class of S-MJSs are firstly presented, and then in the input-output framework the memory controller and filter synthesis are developed for S-MJSs with time-varying delay. Furthermore, the analysis and synthesis problems for a class of complex S-MJSs with several kinds of typical limited information, which refer to parametric uncertainties, controller and sensor saturation or failure, etc. In addition, the proposed approaches will be applied to the fault detection and tolerant control of marine gas turbine. The goal of this project is to develop systematic methods for the stability analysis, controller design and filter synthesis of S-MJSs, which will improve and consummate the existing control and filtering theory of S-MJSs.