Geometric Characterization of Strictly Positive Real Regions and its Applications

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dc.creatorWang, Long
dc.creatorYu, Wensheng
dc.date2002-02-23
dc.date.accessioned2026-07-07T04:46:38Z
dc.date.available2026-07-07T04:46:38Z
dc.descriptionStrict positive realness (SPR) is an important concept in absolute stability theory, adaptive control, system identification, etc. This paper characterizes the strictly positive real regions in coefficient space and presents a robust design method for SPR transfer functions. We first introduce the concepts of SPR regions and weak SPR regions and show that the SPR region associated with a fixed polynomial is unbounded, whereas the weak SPR region is bounded. We then prove that the intersection of several weak SPR regions associated with different polynomials can not be a single point. Furthermore, we show how to construct a point in the SPR region from a point in the weak SPR region. Based on these theoretical development, we propose an algorithm for robust design of SPR transfer functions. This algorithm works well for both low order and high order polynomial families. Illustrative examples are provided to show the effectiveness of this algorithm.
dc.descriptionSome new properties of strict positive realness are derived
dc.identifierhttps://arxiv.org/abs/math/0202240
dc.identifierhttp://arxiv.org/abs/math/0202240
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63413
dc.subjectOptimization and Control
dc.subjectDynamical Systems
dc.subject93B35; 93C40
dc.titleGeometric Characterization of Strictly Positive Real Regions and its Applications
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