不确定随机线性重复过程的鲁棒H_∞滤波

Robust H_∞ Filtering of Uncertain Stochastic Linear Repetitive Processes

研究鲁棒滤波优化问题,随机线性重复过程是具有实际意义的特殊二维系统。针对二维系统研究鲁棒H∞滤波稳定性和误差问题,通过设计一个全阶滤波器使不确定随机线性重复过程均方渐近稳定,给出鲁棒H∞全阶滤波器存在的充分条件,并将滤波器的设计转化为一个凸优化的求解问题。所设计的滤波器能够保证相对于所有能量有界的外界扰动信号,重复过程的H∞性能指标小于一定值γ。另外,将所得结果扩展到过程参数具有范数有界不确定性和凸多面体不确定性的系统中。仿真结果证明了设计方法的有效性。

The paper investigates the problem of H_∞ filtering for a class of stochastic linear repetitive processes,which are a distinct class of 2D linear systems of both system theoretic and application interest.Attention is focused on the design of full-order filter guaranteeing mean-square asymptotically stable and a prespecified H_∞ performanceγfor the filtering error processes with respect to all energy-bounded input signals.Sufficient conditions are proposed in terms of linear matrix inequality,and the corresponding filter design is cast into a convex optimization problem.In addition,the results obtained are further extended to more general cases where the repetitive processes matrices contain norm-bounded uncertainty and polytopic uncertainty.The efficiencies of the proposed design scheme are demonstrated via a numerical example.