Uniform Asymptotic Stability of Solutions of Fractional Functional Differential Equations [PDF]
Abstract and Applied Analysis, 2013 Some global existence and uniform asymptotic stability results for fractional functional differential equations are proved.
Yajing Li, Yejuan Wang
doaj +4 more sources
Lyapunov functions for linear nonautonomous dynamical equations on time scales [PDF]
Advances in Difference Equations, 2006 The existence of a Lyapunov function is established following a method of Yoshizawa for the uniform exponential asymptotic stability of the zero solution of a nonautonomous linear dynamical equation on a time scale with uniformly bounded graininess.
Zmorzynska Alexandra, Kloeden Peter E
doaj +3 more sources
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 ′ ( t ) = F ( t , x t ) {x’}(t) = F(t,{x_t}) and obtain conditions on a Liapunov functional to ensure the ...
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 ′ ( t ) = F ( t , x t ) x’(t) = F(t,{x_t}) and obtain conditions on a Liapunov functional to insure the uniform asymptotic stability ...
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