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On the algebraic Lyapunov inequality
Pollack Periodica, 2015Considering the continuous algebraic Lyapunov inequality and equation PA + A*P<0 , PA + A*P=Q, the aim of this paper is to give an algebraic proof of the Lyapunov theorem through mathematical induction. Moreover by the presented algorithm all positive definite solutions of the Lyapunov equation are given in the case, if the right hand side is ...
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Inertia theorems for operator Lyapunov inequalities
Systems & Control Letters, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sasane, AJ, Curtain, RF
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Lyapunov Inequalities and their Applications
2000For nearly 50 years Lyapunov inequalities have been an important tool in the study of differential equations. In this survey, building on an excellent 1991 historical survey by Cheng, we sketch some new developments in the theory of Lyapunov inequalities and present some recent disconjugacy results relating to second and higher order differential ...
Richard C. Brown, Don B. Hinton
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From Lyapunov Functions to Sobolev Inequalities
Theory of Probability & Its Applications, 2015Summary: Based on the existence of the Lyapunov functions, the weak and local Lyapunov-\(\Psi\)-Sobolev type inequalities which yield the convergence rates of semigroup are considered.
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2013
In this chapter we give some proofs of Lyapunov’ inequality, in both the linear and nonlinear contexts.
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In this chapter we give some proofs of Lyapunov’ inequality, in both the linear and nonlinear contexts.
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2013
Introduction The eigenvalue problems for quasilinear and nonlinear operators present many differences with the linear case, and a Lyapunov inequality for quasilinear resonant systems showed the existence of eigenvalue asymptotics driven by the coupling of the equations instead of the order of the equations.
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Introduction The eigenvalue problems for quasilinear and nonlinear operators present many differences with the linear case, and a Lyapunov inequality for quasilinear resonant systems showed the existence of eigenvalue asymptotics driven by the coupling of the equations instead of the order of the equations.
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Some Elementary Variations of the Lyapunov Inequality
SIAM Journal on Applied Mathematics, 1978A moment inequality derived by Petrov [1] is shown to follow from the classical Lyapunov inequality applied to a certain conditional distribution. A general conditional version of the Lyapunov inequality is presented. The performance of the Petrov inequality is compared with that of a related tighter inequality (also obtained by conditioning) in the ...
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Verification Methods for the Lyapunov–Krasovskii Functional Inequalities
SIAM Journal on Control and OptimizationzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ali Diab 0002 +2 more
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On Lyapunov Inequalities and Subsolutions for Efficient Importance Sampling
ACM Transactions on Modeling and Computer Simulation, 2012In this article we explain some connections between Lyapunov methods and subsolutions of an associated Isaacs equation for the design of efficient importance sampling schemes. As we shall see, subsolutions can be derived by taking an appropriate limit of an associated Lyapunov inequality.
Jose H. Blanchet +2 more
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An explicit solution to the generalized Lyapunov matrix inequality
Systems & Control LetterszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mario Spirito, Daniele Astolfi
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