转移概率未知下Markov线性切换系统的H_∞控制

H_∞ Control for Markov Switching Model with Unknown Transfer Probabilities

研究了一类具有Markov特性的随机时延切换系统的H_∞控制问题。具体针对切换系统数据传输的随机时延特性,将随机时延转换成一类转移概率未知的Markov序列,基于模态依赖型Lyapunov函数设计了模态依赖状态反馈控制器。在此基础上,通过求解线性矩阵不等式(LMI),得到了使控制系统渐近稳定且具有H_∞性能充分条件。数值算例表明,该设计方法有效。

This paper deals with the class of H ∞ control problems of stochastic time-delay network system with Markov chain. For network switching system, the random delay is transformed into a Markov chain with unknown transfer probability and a state dependent state feedback controller is designed. The sufficient condition of the closed loop feedback control system which guarantees the disturbance rejection with a desired H ∞ performance can be obtained by solving the LMI. Numerical examples are employed to show the usefulness of the proposed results.