Titlebook: Set-Theoretic Methods in Control; Franco Blanchini,Stefano Miani Book 2015Latest edition Springer International Publishing Switzerland 201

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2324-9749 cessary for the adequate formulation and statement of the main concepts, yet allowing for a detailed exposition of the numerical algorithms for the solution of the proposed problems..Set-Theoretic Methods in Co978-3-319-33048-8978-3-319-17933-9Series ISSN 2324-9749 Series E-ISSN 2324-9757

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Lyapunov and Lyapunov-like functions,ic notions of Lyapunov and Lyapunov-like functions will be presented. Before introducing the main concept, a brief presentation of the class of dynamic models will be considered and some preliminary mathematical notions are given.

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Convex sets and their representation,etailed exposition on convexity, the reader is referred to specialized literature (Rockafellar, Convex analysis, Princeton University Press, Princeton, 1970; Rockafellar and Wets, Variational analysis, Springer, New York, 1998; Boyd and Vandenberghe, Convex optimization, Cambridge University Press,

essential-fats

Invariant sets,ncept is at the basis of many control schemes that will be considered later. Such a concept naturally arises when dealing with Lyapunov functions, as we have seen, since any Lyapunov function has positively invariant sublevel sets. However, the invariance concept does not require the introduction of

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Control of parameter-varying systems,roperly introduce the results, let us reconsider the stability analysis problem for an uncertain system of the form . where ., with . compact, and .(⋅ ) is continuous. In the case of a single stable linear system, stability is equivalent to the fact that the eigenvalues of . have negative real part