Periodicity, Detectability and the Matrix Riccati Equation
Periodicity, Detectability and the Matrix Riccati Equation
复制标题
周期性、可检测性和矩阵 Riccati 方程
DOI：
10.1137/0313077
复制
发表时间：
1975
期刊：
影响因子：
--
通讯作者：
G. Hewer
中科院分区：
文献类型：
--
作者：
G. Hewer
讨论了具有周期系数的矩阵Riccati微分方程的周期解。这种方程出现在线性滤波和控制以及许多其他应用中。主要结果是：周期解的存在性等价于某些系数对的可检测性和可镇定性。这个结果推广了代数Riccati方程的Kalman-Wonham-Kucera定理。在众多的讨论中，有一个关于线性周期控制系统的可检测性的讨论，显然是新的。另一个重要的结果，对于线性矩阵微分方程，是有界解，指数稳定解和周期解的等价性。最后，周期解是卡尔曼意义下的平衡解。
This paper discusses the periodic solution of matrix Riccati differential equations with periodic coefficients. Such equations arise in linear filtering and control and in many other applications. The principal result: the existence of a periodic solution is equivalent to detectability and stabilizability of certain coefficient pairs. This result generalizes the Kalman–Wonham–Kucera theorem for algebraic Riccati equations. Among the numerous preliminaries is a discussion, apparently new, of detectability for linear periodic control systems. Another important result, for a linear matrix differential equation, is the equivalence of a bounded solution, an exponentially stable solution and a periodic solution. Finally, the periodic solution is shown to be an equilibrium solution in the sense of Kalman.