奇异摄动Markov跳变时滞系统作为一类具有复杂结构的随机时滞系统，能反映出随机混杂系统的跳变特性和奇异摄动特性等许多本质特征，故更能准确地表征一些实际系统模型。本项目拟开展奇异摄动Markov跳变时滞系统的多目标鲁棒控制与滤波问题研究，旨在提供行之有效的多目标鲁棒控制器与滤波器的存在条件与设计方法。从奇异摄动特性出发，探求奇异摄动特性和跳变特性对系统性能的影响，利用分频混合设计方法、广义KYP(Kalman-Yakubovich-Popov)引理、随机分析、均一化设计理念以及新奇的时滞处理技术给出一些低保守性、易于验证的多种性能判据并存的时滞相关条件。另外，给出相应的满足多种性能指标的鲁棒控制器/滤波器设计方法，并进一步协同优化所得设计方法的保守性与计算复杂度。本项目的实施，进一步丰富了奇异摄动Markov跳变时滞系统理论体系，并为该系统在电力系统的网络化分析与控制中的应用提供新的依据。

As a kind of stochastic delayed systems with complex structure, singular perturbed Markov jump delayed systems can reflect many essential characteristics of stochastic hybrid systems, such as jumping characteristic and singular perturbation characteristic. Therefore, it can more accurately characterize some practical system models. This project is concerned with the multi-objective robust control and filtering problems for singularly perturbed Markov jump delayed systems. Its aims are to establish the available conditions for the existence of admissible controllers/filters and provide the corresponding design methods. Based on the singular perturbed characteristics, the influences of singular perturbation and jumping characteristics on system performance are fully explored. By using the frequency decomposition design method, generalized KYP (Kalman-Yakubovich-Popov) Lemma, stochastic analysis theory, homogeneous design concept and some novel techniques in processing delay-dependent issues, some delay-dependent conditions for the existence of multiple performance criteria, which are less conservative and easy-to-verify, are obtained. With the help of those criteria, the corresponding robust controller/filter design methods satisfying various performance indexes are given, in which the conservativeness and computational complexity are further optimized together. The implementation of this project will further develop and enrich the theory of singular perturbed Markov jump delayed systems, and provide a new reference for the application of such systems in the analysis and control of networked power systems.