具有不确定转移速率的广义马尔可夫跳变系统的耗散模糊控制

Dissipative Fuzzy Control for Singular Markovian Jump Systems with Generally Uncertain Transition Rates

研究了具有不确定转移速率的广义马尔可夫跳变系统的耗散模糊控制问题.首先,建立了一个新的李雅普诺夫函数,进而得到了能够保证系统随机可容许并且具有给定耗散性能指标α的有界实引理.利用时滞分割方法和新的不等式去处理函数,从而在一定程度上减少了结论的保守性.其次,基于这些因素,得到了可以利用严格的线性矩阵不等式求解的期望控制器的显式表达式.在设计控制器的过程中,将不确定转移速率分为两种情况,进而得到了两种不同情况下的线性矩阵不等式.最后,一些数值算例反映出本文方法具有较小的保守性和有效性.

The problem of dissipative fuzzy control for singular Markovian jump systems is studied with generally uncertain transition rates.Firstly,a new Lyapunov-Krasovskii functional is established to develop the new bounded real lemma(BRL)which guarantee the system to be stochastically admissible with given dissipative performanceα.Delay decomposition approach and new inequality to deal with functional are used,which can reduce the conservatism to a certain extent.Secondly,based on these ingredients,the explicit expression of the desired controller is obtained by solving a set of strict linear matrix inequalities(LMIs).In the design process of the controller,the generally uncertain transition rates are divided into two cases,and then obtain the LMIs in two different cases.Finally,some numerical examples reflect the less conservatism and effectiveness of the method in this article.