离散马尔科夫跳跃线性系统的非脆弱H_∞滤波

Non-fragile H_∞ filtering for discrete-time Markovian jumping linear systems

针对一类离散有限模态马尔科夫跳跃线性系统(MJLs)的滤波问题,进行了具有乘性范数有界参数摄动的模态不依赖 H_∞非脆弱滤波器的设计研究。基于随机内部均方稳定(IMSS)理论,采用线性矩阵不等式(LMI)技术,给出了模态不依赖 H_∞非脆弱滤波器存在的充分条件和设计方法;利用线性矩阵不等式的仿射特性,先将设计方法推广到跳变转移概率具有凸多面体不确定时的鲁棒模态不依赖 H_∞非脆弱滤波器设计,然后进一步拓展到考虑系统参数具有凸多面体不确定时的鲁棒模态不依赖 H_∞非脆弱滤波器设计,最后通过算例数值仿真表明了所得结论的有效性。

In view of the filtering problem of a class of discrete-time finite-state Markovian jumping linear systems （MJLs）, this paper investigates the design of the mode-independent H∞ non-fragile filter with multiplicative norm-bounded parameter variation. Based on the stochastic internally mean square stability （IMSS） theory, the sufficient condition on the existence of the mode-independent H∞ non-fragile filter in terms of linear matrix inequalities （LMIs）, together with the filter design approach, is provided. With the arlene property of LMI, the previous result is first extended to the case where there exits polytopic uncertainty in the transition probability matrix of the Markov chain and the corresponding design approach for the robust H∞ non-fragile filter is readily obtained. Then, considering the presence of polytopic uncertainties of the system matrices, another further extension to designing the robust H∞ non-fragile filter is made. In the end, a numerical example is presented to illustrate the validity of the results in this paper.