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On almost Lyapunov functions [PDF]
53rd IEEE Conference on Decision and Control, 2014 We study asymptotic stability properties of nonlinear systems in the presence of “almost Lyapunov” functions which decrease along solutions in a given region not everywhere but rather on the complement of a set of small volume. Nothing specific about the structure of this set is assumed besides an upper bound on its volume.
Charles Ying +2 more
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A Lyapunov Function for an Extended Super-Twisting Algorithm
IEEE Transactions on Automatic Control, 2018Recently, an extension of the super-twisting algorithm for relative degrees $m\geq {}1$ has been proposed. However, as of yet, no Lyapunov functions for this algorithm exist.
Richard Seeber +2 more
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Lyapunov Functions and Cone Families [PDF]
Journal of Statistical Physics, 2012 We describe systematically the relation between Lyapunov functions and nonvanishing Lyapunov exponents, both for maps and flows. This includes a brief survey of the existing results in the area. In particular, we consider separately the cases of nonpositive and arbitrary Lyapunov functions, thus yielding optimal criteria for negativity and positivity ...
Claudia Valls +2 more
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Generalized Lyapunov functions and functional equations [PDF]
Annali di Matematica Pura ed Applicata, 1965 Some results of Minty and Browder on the existence of solutions of functional equations are generalized by replacing the notion of monotony by one involving a Lyapunov function. In the last section, analogous arguments are used to obtain an existence theorem for an initial value problem belonging to an ordinary differential equation on Hilbert space.
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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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Rendiconti del Circolo Matematico di Palermo, 2004
The paper is related to the classical theorem of Lyapunov which says that an \(R^n\)-valued atomless \(\sigma\)-additive measure on a \(\sigma\)-algebra has a convex range. \textit{G. Knowles} [SIAM J. Control 13, 294--303 (1974; Zbl 0302.49005)] generalized this theorem for non-injective measures with values in locally convex spaces. \textit{P.
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The paper is related to the classical theorem of Lyapunov which says that an \(R^n\)-valued atomless \(\sigma\)-additive measure on a \(\sigma\)-algebra has a convex range. \textit{G. Knowles} [SIAM J. Control 13, 294--303 (1974; Zbl 0302.49005)] generalized this theorem for non-injective measures with values in locally convex spaces. \textit{P.
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Hamiltonian-type Lyapunov functions
IEEE Transactions on Automatic Control, 1983A flexible and systematic way for the construction of Lyapunov functions which lends itself to the use of nonlinear programming techniques is presented. The class of Lyapunov functions obtained is shown to be energy functions (Hamiltonians) for an equivalent system.
R. Marino, S. Nicosia
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Constructions of Strict Lyapunov Functions
2009The construction of strict Lyapunov functions is a challenging problem that is of significant ongoing research interest. Although converse Lyapunov function theory guarantees the existence of strict Lyapunov functions in many situations, the Lyapunov functions that converse theory provides are often abstract and nonexplicit, and therefore may not lend ...
Malisoff, Michael, Mazenc, Frédéric
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Attractors and Lyapunov Functions
2020The main tool in estimating dimensions of invariant sets and entropies of dynamical systems developed in this book is based on Lyapunov functions. In this chapter we introduce the basic concept of global attractors. The existence of a global attractor for a dynamical system follows from the dissipativity of the system.
Volker Reitmann, Nikolay Kuznetsov
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Higher Derivatives of Lyapunov Functions [PDF]
Differential Equations, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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