一类转移概率部分未知的离散跳变系统的控制

施蒋彬　谢纬安

摘 要：讨论了一类转移概率部分未知的离散Markov跳变系统的控制问题，针对有外界未知干扰，设计了基于观测器的优化鲁棒控制器。基于鲁棒控制理论，通过对重构的观测器系统的分析，提出了使得系统随机稳定且满足性能控制器存在条件。结合构造的Lyapunov和線性矩阵不等式变换，给出了控制器的设计方法。设计的控制器具有随机稳定性，抗干扰能力强。仿真示例说明了设计方法的有效性。

关键词：离散跳变系统 性能 控制器

Control of a Class of Discrete Jumping Systems with Partially Unknown Transition Probabilities

Shi Jiangbin Xie Weian

Abstract：The article discusses the control problem of a discrete Markov jump system with a partially unknown transition probability. Aiming at the unknown external interference， an optimized robust controller based on the observer is designed. Based on the robust control theory， through the analysis of the reconstructed observer system， the article proposes to make the system stochastically stable and satisfy the existence conditions of the performance controller. Combining the constructed Lyapunov and linear matrix inequality transformation， the design method of the controller is given. The designed controller has random stability and strong anti-interference ability. The simulation example illustrates the effectiveness of the design method.

Key words：discrete jump system， performance， controller