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

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.