Qualitative analysis of a mechanical system of coupled nonlinear oscillators
Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper we investigate nonlinear systems of second order ODEs describing the dynamics of two coupled nonlinear oscillators of a mechanical system. We obtain, under certain assumptions, some stability results for the null solution.
Gheorghe Moroșanu +1 more
doaj +1 more source
On the Ψ−uniform asymptotic stability of nonlinear Lyapunov matrix differential equations [PDF]
ITM Web of Conferences, 2022 This paper deals with obtaining (necessary and) sufficient conditions for Ψ− uniform asymptotic stability of solutions of nonlinear Lyapunov matrix differential equations.
Diamandescu Aurel
doaj +1 more source
Heliyon, 2021 This paper presents asymptotic behaviour of solution to certain nonlinear nonautonomous neutral functional differential equation of the third order. The third order functional differential equation is cut back to system of first order and used together ...
Adeleke Timothy Ademola
doaj +1 more source
Counterexample to a Lyapunov Condition for Uniform Asymptotic Partial Stability [PDF]
IEEE Control Systems Letters, 2020 Partial stability characterizes dynamical systems for which only a part of the state variables exhibits a stable behavior. In his book on partial stability, Vorotnikov proposed a sufficient condition to establish this property through a Lyapunov-like function whose total derivative is upper-bounded by a negative definite function involving only the sub-
Jakub Orlowski +2 more
openaire +3 more sources
An Asymptotic Stability and a Uniform Asymptotic Stability for Functional Differential Equations [PDF]
Proceedings of the American Mathematical Society, 1993 We consider a system of functional differential equation x ′
openaire +2 more sources
On asymptotic output stability for delay differential systems [PDF]
Известия высших учебных заведений: Прикладная нелинейная динамикаThe purpose of this study is to obtain sufficient conditions for output asymptotic stability of nonlinear nonautonomous time-delay systems described by ordinary differential equations.
Sedova, Natalia Olegovna
doaj +1 more source
On the uniform asymptotic stability in functional-differential equations [PDF]
Proceedings of the American Mathematical Society, 1982 We consider a system of functional differential equations x ′ (
openaire +2 more sources
Lyapunov conditions for uniform asymptotic output stability and a relaxation of Barbălat’s lemma [PDF]
Automatica, 2021 Asymptotic output stability (AOS) is an interesting property when addressing control applications in which not all state variables are requested to converge to the origin. AOS is often established by invoking classical tools such as Barbashin-Krasovskii-LaSalle's invariance principle or Barbalat's lemma.
Iasson Karafyllis, Antoine Chaillet
openaire +3 more sources
Preservation of uniform asymptotic stability under perturbations [PDF]
Proceedings of the American Mathematical Society, 1975 Suppose the trivial solution of the interval initial value problem for a linear, convolution, Volterra integrodifferential equation is uniformly asymptotically stable. If the kernel in this equation is integrable, then it is shown that this stability is preserved under perturbations which are nonantisipative and of order two or more.
openaire +2 more sources
New Fundamental Results on the Continuous and Discrete Integro-Differential Equations
Mathematics, 2022 This work studies certain perturbed and un-perturbed nonlinear systems of continuous and discrete integro-delay differential equations (IDDEs). Using the Lyapunov–Krasovskii functional (LKF) method and the Lyapunov–Razumikhin method (LRM), uniform ...
Osman Tunç +3 more
doaj +1 more source