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The concept of “strict positive realness” of the rational transfer functions extensively used in various field of control. The basic definition of strict positive realness is motivated by Popov’s hyperstability theory and is stated in the frequency domain. With expiry fourth decade, still there is not unique statement which states the necessary and sufficient conditions for strict positive realness in the control literatures.
In this paper 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.