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Automated tight Lyapunov analysis for first-order methods
We present a methodology for establishing the existence of quadratic Lyapunov inequalities for a wide range of first-order methods used to solve...
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Guiding Functional Families, Lyapunov Vector Functions, and the Existence of Poisson Bounded Solutions
In this paper, we use the method of guiding functional families and the method of Lyapunov vector functions for establishing a sufficient condition...
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An accelerated lyapunov function for Polyak’s Heavy-ball on convex quadratics
In 1964, Polyak showed that the Heavy-ball method, the simplest momentum technique, accelerates convergence of strongly-convex problems in the...
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On the structure of the infinitesimal generators of scalar one-dimensional semigroups with discrete Lyapunov functionals
Dynamical systems generated by scalar reaction-diffusion equations on an interval enjoy special properties that lead to a very simple structure for...
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On the Method of Lyapunov Functionals for a Linear First-Order Volterra Integrodifferential Equation with Delay on the Semiaxis
AbstractSufficient conditions are established to ensure the estimation, boundedness, power-law absolute integrability on the semiaxis, the tendency...
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The Method of Lyapunov Functionals and the Boundedness of Solutions and Their First and Second Derivatives for a Third-Order Linear Equation of the Volterra Type on the Half-Line
AbstractSufficient conditions are established for the boundedness of all solutions and their first two derivatives of a third-order linear...
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New Results on the Qualitative Analysis of Solutions of Vides by the Lyapunov–Razumikhin Technique
A new mathematical model described by a Volterra integrodifferential equation (VIDE) with constant delay is examined. New agreeable conditions on the...
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Time-averaging principle for G-SDEs based on Lyapunov condition
In this paper, we tame the uncertainty about the volatility in time-averaging principle for stochastic differential equations driven by G-Brownian...
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Mittag-Leffler stability and Lyapunov stability for a problem arising in porous media
A fractional order problem arising in porous media is considered. Well-posedness as well as stability are discussed. Mittag-Leffler stability is...
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Lyapunov Stability and Economic Analysis of Monkeypox Dynamics with Vertical Transmission and Vaccination
Monkeypox is a zoonosis currently emerging and reemerging in some parts of the world. Though the disease is primarily transmitted to humans from...
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Structural Spectral Methods for Solving Continuous Lyapunov Equations
AbstractFor linear multivariable continuous stationary stable control systems with a simple spectrum, presented in the form of a canonical diagonal...
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Generalized Lyapunov Exponents and Aspects of the Theory of Deep Learning
We discuss certain recent metric space methods and some of the possibilities these methods provide, with special focus on various generalizations of...
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The Rionero’s special type of Lyapunov function and its application to a diffusive epidemic model with information
We consider a SIR-like reaction-diffusion epidemic model which embeds opinion-driven human behavioural changes. We assume that the contagion rate is...
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Stability Analysis of Additive Time-Varying T–S Fuzzy System Using Augmented Lyapunov Functional
This article discusses the stability analysis problem of Takagi–Sugeno (T–S) fuzzy system with additive time-varying delay components. To find a...
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An application of Lyapunov–Razumikhin method to behaviors of Volterra integro-differential equations
This work presents some extensions and improvements of former results that allow proving asymptotic stability, uniform stability and global uniform...
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On the Controllability of Entropy Solutions of Scalar Conservation Laws at a Junction via Lyapunov Methods
In this note, we prove a controllability result for entropy solutions of scalar conservation laws on a star-shaped graph. Using a Lyapunov-type...
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High order approximations of the operator Lyapunov equation have low rank
We present a low-rank greedily adapted hp -finite element algorithm for computing an approximation to the solution of the Lyapunov operator equation....
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New Lyapunov-Krasovskii Functional for Stability Analysis of Linear Systems with Time-Varying Delay
This paper focuses on the problem of delay-dependent stability of linear systems with time-varying delay. A new delay-product-type augmented...