离散传递函数正实性与连续传递函数有限频率正实性的代数判据

Algebraic Criteria for Positive Realness of Discrete Transfer Function and Finite Frequency Positive Realness of Continuous Transfer Function

正实性是控制理论中最重要的概念之一.许多控制目标的实现皆依赖于某些传递函数的正实性.相比于正实性,有限频率正实性则是较近提出的概念,并且亦在控制理论中找到了大量应用.为了判断离散标量传递函数的正实性和连续标量传递函数的有限频率正实性,本文分别给出了一种易于计算的简洁代数判据.现有的判断连续标量传递函数严格正实性的代数判据可以看作是本文结果的特殊情况.数值算例验证了方法的有效性.

Positive realness of a transfer function is one of the most important notions in control theory. The achievements of many control objectives rely on the positive realness of certain transfer functions. Compared with positive realness, finite frequency positive realness is a new notion, and it also finds some important applications in control theory. In order to verify the positive realness of scalar discrete transfer function and the finite frequency positive realness of continuous scalar transfer function, this paper presents a simple algebraic criterion. Some existing results can be regarded as special cases of the presented results. Numerical examples show the effectiveness of the proposed approach.