Titlebook: Homogeneous Polynomial Forms for Robustness Analysis of Uncertain Systems; Graziano Chesi,Andrea Garulli,Antonio Vicino Book 2009 Springer

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Positivity Gap,roviding a parametrization of the set of PNS forms. It is shown that the set of PNS forms is dense in the space of forms, that each PNS form is the vertex of a cone of PNS forms, and how PNS forms can be constructed via the SMR.

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Robustness with Time-varying Uncertainty, to the tools for checking positivity of forms introduced in Chapters 1 and 2, the construction of such Lyapunov functions can be formulated in terms of special convex optimizations problems. Both polytopic systems and LFRs are considered. Several robustness performance measures are also investigated.

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Robustness with Bounded-rate Time-varying Uncertainty,ch includes the classes of HPLFs and HPD-QLFs as special cases. It is shown that the construction of HPD-HLFs for assessing robust stability as well as computing robust stability margins can be tackled via convex optimizations constrained by LMIs through the use of the SMR of matrix forms.

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Lecture Notes in Control and Information Scienceshttp://image.papertrans.cn/h/image/428118.jpg

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https://doi.org/10.1007/978-1-84882-781-3Control Engineering; Hilbert’s 17th Problem; Robust Analysis; Robust Control; SOS Polynomials; Time-invar

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Homogeneous Polynomial Forms for Robustness Analysis of Uncertain Systems978-1-84882-781-3Series ISSN 0170-8643 Series E-ISSN 1610-7411

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0170-8643 Overview: Allows the reader to increase the robustness of control systems subject to uncertainties thanks to striking advances in convex optimization.Draws together a number of well-established tools in control978-1-84882-780-6978-1-84882-781-3Series ISSN 0170-8643 Series E-ISSN 1610-7411