不确定线性时变时滞系统的鲁棒H_∞滤波

Robust H_∞ filtering for uncertain linear systems with time-varying delay

研究一类不确定线性连续时滞系统的改进鲁棒H∞滤波问题.采用时滞分解方法,构造一种新的Lyapunov-Krasovskii泛函,并基于一种积分不等式讨论了确定性系统的H∞性能分析问题.然后,借助于线性化技术,以线性矩阵不等式(LMI)的形式给出了滤波器存在的充分条件,并将确定性系统滤波器设计方法扩展到凸多面体不确定性情形.最后通过仿真算例说明了该方法的有效性.

The problem of improved robust H∞ filtering for a class of uncertain linear continuous-time systems is studied. By applying the idea of delay decomposition, a new Lyapunov-Krasovskii functional is constructed. And based on an integral inequality, an H∞ performance analysis criterion for the filtering error system is firstly derived. Then by using a linearsiation technique, the filter synthesis is developed. It is shown that the filter gains can be obtained by solving a set of linear matrix inequalities（LMIs）. Moreover, immediate extensions of the results are made to systems with polytopic uncertainties. Finally, two examples are given to illustrate the effectiveness of the proposed method.