连续时间马尔可夫跳变系统多频段多指标控制

Multi-frequency and Multi-performance Control for Continuous-time Markov Jump Systems

针对连续时间马尔可夫跳变系统,基于有限频段理论设计使系统在不同频段下满足不同性能指标的状态反馈控制器.由于系统在不同模态下具有随机马尔可夫跳变特性,使得针对确定系统的有限频段问题难以直接应用.本文将跳变系统各模态进行增广从而得到带有跳变率的增广线性系统.针对该确定系统,本文基于广义KYP(Kalman-Yakubovich-Popov)引理,在不同频段下设计状态反馈控制器,使原跳变系统镇定并在不同频段下满足不同的性能指标.本文所提控制方案为马尔可夫跳变系统等混杂系统的有限频段问题研究提供了新的思路.

Based on the finite-frequency theory,in this study,we designed a state feedback controller for continuous-time Markov jump systems to satisfy their multiple frequency performance requirements. Due to the stochastic Markov jumping among different modes,the finite-frequency specification for deterministic systems cannot be directly used in jump systems. In this paper,by augmenting the modes of Markov jump systems,we transform the original jump systems into augmented deterministic systems with transition probabilities.Then,based on the generalized KYP lemma,we designed a state feedback controller to stabilize the jump systems to enable them to meet the multi-frequency and multi-performance requirements. The proposed methodology provides a new approach to the finite frequency problems of the hybrid generalized KYP lemma.