离散系统方差约束鲁棒H_2/H_∞滤波的新算法

New algorithm for robust H-two/H-infinity filtering with variance constraints for discrete-time systems

考虑带有稳态误差方差约束的线性受扰系统的鲁棒H2/H∞滤波问题.引入了广义逆矩阵,提出了一个新的算法.通过直接解两个Riccati方程后,获得滤波器,并且同时满足3个性能要求:滤波过程是渐近稳定的;每个状态的稳态估计误差方差不超过规定的上界;从外部噪声输入到误差状态输出的传递函数的H∞范数满足规定的上界.一个数字例子说明了这种设计方法的有效性.

The robust H-two/H-infinity filtering problem for linear perturbed systems with steady-state error variance constraints is considered. The generalized inverse technique of matrix is introduced, and a new algorithm is developed. After two Riccati equations are solved, the filter can be obtained, and the following three performance requirements are simultaneously satisfied: The filtering process is asymptotically stable; The steady-state variance of the estimation error of each state is not more than the individual prespecified upper bound; The transfer function from exogenous noise inputs to error state outputs meets the prespecified Hnorm upper bound constraint. An numerical example is provided to demonstrate the flexibility of the proposed design approach.