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On quadratic lyapunov functions
IEEE Transactions on Automatic Control, 2003A topological structure, as a subset of [0,2/spl pi/)/sup L//spl times//spl Ropf//sub +//sup n-1/, is proposed for the set of quadratic Lyapunov functions (QLFs) of a given stable linear system. A necessary and sufficient condition for the existence of a common QLF of a finite set of stable matrices is obtained as the positivity of a certain integral ...
Daizhan Cheng +2 more
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Control Minkowski–Lyapunov functions
Automatica, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Optimization of lyapunov functionals
Meccanica, 1975The problem of optimality of Lyapunov Functionals is posed in terms of the requirements of a specific problem. The optimizationprocess is based on a method used to construct Lyapunov Functionals called “Path Integral Synthesis” proposed by the authors.
Golia, Carmine, Abel, Jacob M.
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Lyapunov functionals and matrices
Annual Reviews in Control, 2010Abstract In this contribution we present some basic results concerning the computation of quadratic functionals with prescribed time derivatives for linear time delay systems. Some lower and upper bounds for the functionals are given. The functionals are defined by special matrix valued functions. These functions are called Lyapunov matrices.
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Robust Minkowski–Lyapunov functions
Automatica, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the Construction of Lyapunov Functions
SIAM Journal on Applied Mathematics, 1969the same. These results are used to obtain new instability results for the Hill equation which extend the classical results of Lyapunov and Haupt. Finally, we show that a Lyapunov function for w' = 2Bw can be used to algorithmically obtain a Lyapunov function for y' = By along with certain verifiable conditions from which stability properties of y ...
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Founded Lyapunov–Bogdanov Functionals
Differential Equations, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Borukhov, V. T., Kvetko, O. M.
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Lyapunov and Lyapunov-like functions
2007Lyapunov functions are crucial in the present book aims, given the strict relation between Lyapunov functions and invariant sets. In this chapter, basic 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 ...
Franco Blanchini, Stefano Miani
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Weak Converse Lyapunov Theorems and Control-Lyapunov Functions
SIAM Journal on Control and Optimization, 2004Summary: Given a weakly uniformly globally asymptotically stable closed (not necessarily compact) set \({\mathcal A}\) for a differential inclusion that is defined on \(\mathbb{R}^n\), is locally Lipschitz on \(\mathbb{R}^n \backslash{\mathcal A}\), and satisfies other basic conditions, we construct a weak Lyapunov function that is locally Lipschitz on
Christopher M. Kellett, Andrew R. Teel
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Logical composition of Lyapunov functions
International Journal of Control, 2011This article introduces the use of R-functions to compose single Lyapunov functions (LFs) via classic Boolean operators, with the aim to obtain a rich family of non-conventional, generally non-convex functions. The main benefit of the proposed composition is the nice geometric interpretation, since it corresponds to intersection and union operations in
Aldo Balestrino +2 more
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