EXTREME　POINT　RESULTS　FOR　STRICT　POSITIVE　REALNESS　OF　TRANSFER　FUNCTION　FAMILIES

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Several classical results in systems and control field rely on strict positive realness of suitable transfer functions. Absolute stability of nonlinear systems and convergence analysis of adaptive schemes are typical areas where strict positive realness is a key property. In this paper, invariance of this property for families of perturbed transfer functions is studied. Extreme point results are obtained for strict positive realness of polytopic family, multilinear family, and cascade interval family, etc. The concept of critical venices proves to be an important tool to deal with the robustness of control systems with structured uncertainties.