Results 31 to 40 of about 8,963 (248)
On Vector Lyapunov Functions [PDF]
Proceedings of the American Mathematical Society, 1971 It has been proved that the use of a vector Lyapunov function is more advantageous in certain situations rather than a scalar function. Moreover, each function needs to satisfy less rigid requirements. In this paper a new situation has been considered where vector Lyapunov functions play a further useful role. For this purpose, a new type of stability,
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Lyapunov Functionals in Integral Equations
Axioms, 2023 Lyapunov functions/functionals have found their footing in Volterra integro-differential equations. This is not the case for integral equations, and it is therefore further explored in this paper. In this manuscript, we utilize Lyapunov functionals combined with Laplace transform to qualitatively analyze the solutions of the integral equation In ...
Youssef N. Raffoul, Joseph Raffoul
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Learning lyapunov functions for hybrid systems [PDF]
Proceedings of the 24th International Conference on Hybrid Systems: Computation and Control, 2021 We propose a sampling-based approach to learn Lyapunov functions for a class of discrete-time autonomous hybrid systems that admit a mixed-integer representation. Such systems include autonomous piecewise affine systems, closed-loop dynamics of linear systems with model predictive controllers, piecewise affine/linear complementarity/mixed-logical ...
Shaoru Chen +4 more
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, 2023 International audienceThis paper investigates necessary and sufficient Lyapunov conditions for Input-to-State Stability (ISS) of Linear Difference Equations with pointwise delays and an additive exogenous signal.
Auriol, Jean, Bresch-Pietri, Delphine
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Guaranteed Cost Control for a Class of Nonlinear Discrete Time-Delay Systems
IEEE Access, 2019 The guaranteed cost control problem for a class of nonlinear discrete time-delay systems is investigated. Based on the Lyapunov matrix, a complete-type Lyapunov-Krasovskii functional is constructed.
Lanhui Zhang +3 more
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MANAS: Journal of Engineering, 2021 In this manuscript, we consider the first order neutral Volterra integro-differential equation (NVIDE) with delay argument. Firstly, we obtain novel sufficient conditions to establish the asymptotic behaviours of solutions of considered NVIDE using the ...
Yener Altun
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Global dynamics on a class of age-infection structured cholera model with immigration
Electronic Journal of Qualitative Theory of Differential Equations, 2023 This paper is concerned with a class of age-structured cholera model with general infection rates. We first explore the existence and uniqueness, dissipativeness and persistence of the solutions, and the existence of the global attractor by verifying ...
Xin Jiang, Ran Zhang
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Electronic Journal of Qualitative Theory of Differential Equations, 2022 This paper stands for the almost sure practical stability of nonlinear stochastic differential delay equations (SDDEs) with a general decay rate. We establish some sufficient conditions based upon the construction of appropriate Lyapunov functionals ...
Tomas Caraballo +2 more
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Lyapunov stability analysis of higher-order 2D systems
, 2010 We prove a necessary and sufficient condition for the asymptotic stability of a 2D system described by a system of higher-order linear partial difference equations.
Paolo Rapisarda +8 more
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On boundedness, square integrability and uniform stability for neutral non autonomous third order differential equations with delay [PDF]
Mathematica BohemicaIn the study of the solutions for a given class of neutral third order differential equations with delay, a suitable conditions are given based on the Lyapunov second method by considering convenable Lyapunov functional to guarantee the uniform ...
Fatima Abdellaoui, Mebrouk Rahmane
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