误差方差约束下Delta算子不确定系统的鲁棒H∞滤波

研究Delta算子不确定系统在稳态估计误差方差约束下的鲁棒H∞滤波问题.目的是设计滤波器,使得系统在状态矩阵和输出矩阵均存在不确定性时,滤波过程是渐近稳定的,每个状态的稳态估计误差的方差不大于事先给定值,且从噪声输入到误差输出的传递函数满足给定的H∞范数约束.基于矩阵不等式方法,提出了滤波器的存在条件和显式表达式.所得结果可将连续和离散系统的有关结论统一到Delta算子框架.

Robust H∞ filtering for Delta operator formulated uncertain systems with error variance constraints

The problem of robust H∞ filtering for the Delta operator formulated uncertain discrete-time systems with error variance constraints is considered. The purpose is to design a linear filter such that for the system with norm-bound parameter uncertainties in both the state and output matrices, the following three performance requirements are simultaneously satisfied:1) The filtering process is asymptotically stable;2) The steady-state variance of the estimation error of each state is not more than the individual prespecified value;3) The transfer function from the exogenous noise inputs to the error state outputs meets a given H∞ norm upper bound constraint. Sufficient conditions for the filter to meet H∞ performance and steady-state estimation error variance constraints are obtained in terms of algebraic matrix inequality approach, and the explicit expression of the desired filter is also derived. The proposed results can also bring existing H∞ filtering conclusions of continuous-time and discrete-time systems into the unified Delta framework.