误差方差及圆形区域极点约束下状态估计问题的研究：离散时间情形

A Study of Error Variance and Circular Pole-Constrained State Estimation for Discrete-Time Systems

中文关键词  线性离散随机系统  约束方差估计  区域极点配置

英文关键词  linear discrete stochastic systems  constrained variance estimation  circular pole placement  covariance assignment control

中文摘要

      本文研究线性离散随机系统在稳、暂态指标约束下的状态估计问题，即设计滤波增益，使得每个状态的估计误差方差的稳态值不大于预先指定值，同时滤波矩阵的极点位于预先指定的圆形区域内。本文说明上述指标约束可体现于一代数矩阵方程中，并藉此给出期望滤波增益的存在条件及解析表达式。数值例子说明了文中设计方法的直接性与有效性。

英文摘要

      This paper focuses on the problem of state estimation for linear discrete stochastic systems with steady- state and transient performance constraints. The purpose of this problem is to design filter gains such that the steady- state value of the estimation error variance of each state is less than or equal to the prespecified value, and the poles of the filter matrix lie within the prespecified circular region. It is shown that the enforcement of above requirements is related to an algebraic matrix equation. Based on the equation, the existence conditions and the explicit expression of the expected filter gain are given. Finally, a numerical example is provided to demonstrate the directness and efficientness of the design method presented in this paper.