含有不确定性的2维离散线性系统的鲁棒H_2滤波设计

Robust H_2 Filtering Design for 2-D Discrete-time Linear System with Uncertainties

针对含有不确定参数的2维离散线性系统,本文给出了两种鲁棒H2滤波设计方法.第一种方法采用引入参数相关的矩阵函数的思想,所设计的Lyapunov函数及引入的变量都是多项式参数相关的,随着矩阵函数次数的增加条件的保守性逐渐减小.但是次数不能无限增加,当达到一定程度后,即使次数继续增加,条件的保守性不再改变.接着,为了进一步减小保守性,通过详细分析现有条件的保守性来源,给出了第二种方法—循环迭代算法.同现有文献相比,在此算法中引入的变量不需要满足特定的结构,因而具有更小的保守性.最后,通过两个仿真算例证明了当第一种方法无法减小保守性时,第二种方法仍然可以进一步减小保守性.

This paper is about robust H2 filtering design for 2-dimensional discrete-time linear system with convex uncertainties and presents two methods to design the filtering. The first method is based on the idea of introducing parameter-dependent matrix function. As the degree of matrix function increases, more variables are generated to lead to less conservative results. However, the degree can not go infinitely and there exists supremum. The conservatism can not be further reduced when the degree arrives at the supremum. Then, in order to further reduce the conservatism, the second method, i.e., iteration algorithm is proposed based on the analysis of the possible source of conservatism. Since no special structures are required in the slack variables, the algorithm is less conservative than the existing results. In the end, two examples are presented to illustrate that the second method can further reduce conservatism even when the first one fails to do.