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Revision on the Frequency Domain Conditions for Strict Positive Realness

Mojtaba Hakimi Moghaddam and Hamid Khaloozadeh*
International Journal of Control, Automation, and Systems, vol. 5, no. 1, pp.1-7, 2007

Abstract : In this paper, the necessary and sufficient conditions for strict positive realness of the rational transfer functions directly from basic definitions in the frequency domain are studied. A new frequency domain approach is used to check if a rational transfer function is a strictly positive real or not. This approach is based on the Taylor expansion and the Maximum Modulus Principle which are the fundamental tools in the complex functions analysis. Four related common statements in the strict positive realness literature which is appeared in the control theory are discussed. The drawback of these common statements is analyzed through some counter examples. Moreover a new necessary condition for strict positive realness is obtained from high frequency behavior of the Nyquist diagram of the transfer function. Finally a more simplified and completed conditions for strict positive realness of single-input single-output linear time-invariant systems are presented based on the complex functions analysis approach.

Keyword : K.N.Toosi University of Technology

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