基于广义逆理论的区域极点配置研究

在控制理论及应用领域中，区域极点配置一直是控制系统设计的重要方法之一。该文针对线性连续及离散时间系统提出了一种统一的基于广义逆理论的圆形区域极点配置方法，即设计状态反馈控制器，使闭环极点位于给定的圆状区域中。文中给出了期望控制器存在的充要条件及其参数化代数表示。与已有结果相比，该文方法只需求解一线性矩阵方程，因而更易工程实现。数值算例验证的了该方法的有效性及直接性。

Regional Pole Placement Based on Generalized Inverse Theory

In the field of control theory and applications,regional pole placement is always one of the most important methods for designing control systems.In this paper,a unified circular pole placement approach is proposed for both linear continuous and discrete time systems based on the generalized inverse theory.The aim of this approach is to design state feedback controllers such that the closed loop poles are constrained to lie within a specified circular region.This paper gives the sufficient and necessary conditions for the existence of desired controllers as well as the algebraic parametrization of these controllers.Compared to the existing results,the present approach is only required to solve a linear matrix equation,and is thus more suitable for engineering applications.Finally,a numerical example is used to show the effectiveness and directness of the present method.