Results 201 to 210 of about 21,898 (243)
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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.
Daniel Liberzon +2 more
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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.
Daniel Liberzon +2 more
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Ergodic Theory and Dynamical Systems, 2003
Summary: In this paper the Poincaré-Hopf inequalities are shown to be necessary and sufficient conditions for an abstract Lyapunov graph \(L\) to be continued to an abstract Lyapunov graph of Morse type. The Lyapunov graphs considered may represent smooth flows on closed orientable \(n\)-manifolds, \(n\geq 2\).
Bertolim, M. A. +2 more
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Summary: In this paper the Poincaré-Hopf inequalities are shown to be necessary and sufficient conditions for an abstract Lyapunov graph \(L\) to be continued to an abstract Lyapunov graph of Morse type. The Lyapunov graphs considered may represent smooth flows on closed orientable \(n\)-manifolds, \(n\geq 2\).
Bertolim, M. A. +2 more
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Differentiability of Lyapunov Exponents
Journal of Dynamical and Control Systems, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ferraiol, Thiago F. +1 more
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Physical Review E, 2011
The numerically observed approximate functional forms for the transverse and longitudinal-momentum proportional (LP) Gram-Schmidt Lyapunov modes have been studied for some time. We construct a field theory for a system where the number of particles is large enough so the Lyapunov mode contributions from each particle can be considered to change ...
Tony, Chung +2 more
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The numerically observed approximate functional forms for the transverse and longitudinal-momentum proportional (LP) Gram-Schmidt Lyapunov modes have been studied for some time. We construct a field theory for a system where the number of particles is large enough so the Lyapunov mode contributions from each particle can be considered to change ...
Tony, Chung +2 more
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On the multivariate Lyapunov inequalities
Applied Mathematics and Computation, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the Lyapunov Type Inequality
Russian Mathematics, 2020The author's main result concernes an estimate on the zeros of the solutions to a linear equation of the type \[ x''+p(t)x'(t)+q(t)x=0. \] When \(p(t)\) is identically equal to zero, Lyapunov provided the following result: if \(x(t)\) is a solution such that \(x(a)=x(b)=0\) and \(x(t)\ne0\) for every \(t\in(a,b)\), then \[ \int_a^b|q(t)|\,dt\ge\frac{4}{
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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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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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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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The Periodic Lyapunov Equation
SIAM Journal on Matrix Analysis and Applications, 1988Necessary and sufficient conditions for the existence and uniqueness of (positive semidefinite) T-periodic solutions of T-periodic Lyapunov equations in discrete- and continuous-time are given. The proofs are based on the equivalence of these problems to those for certain algebraic Lyapunov equations. Also inertia theorems are included.
BOLZERN, PAOLO GIUSEPPE EMILIO +1 more
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