Estimates of solutions to the linear differential equations of neutral type with several delays of the argument

Демиденко, Г. В.; Vodop’yanov, E. S.; Skvortsova, Maria

doi:10.1134/s1990478913040030

Cited by 5 publications

(6 citation statements)

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“…However, the estimates for exponential decay of solutions to the system (7) established in [7] are weaker than the estimates obtained in [4] if D < 1. These results were strengthened in [9] for a single delay and in [10] for several delays.…”

Section: Theorem 1 Assume That There Exist Matricesmentioning

confidence: 78%

“…Since ⎛ ⎝ y(t) By the notation (8), the matrices S ij , i, j = 1, 2, 3, take the form (10). It is obvious that the positive definiteness of the matrix C implies the positive definiteness of the matrix S. We consider the second and third terms on the right-hand side of (19).…”

Section: Proofmentioning

confidence: 99%

“…In the proof of Theorem 1 in [7], a Lyapunov-Krasovskii functional generalizing the functional (6) to the case of several delays was used:…”

Section: Theorem 1 Assume That There Exist Matricesmentioning

confidence: 99%

“…* To whom the correspondence should be addressed. This paper continues the cycle of works of the authors [2]- [10] devoted to the exponential stability of solutions to systems of differential equations with delay argument. We use the tools of Lyapunov-Krasovskii functionals which are actively applied to obtaining the stability conditions in the theory of equations with delay argument (cf., for example, [1,11,12,13] and the references therein).…”

mentioning

confidence: 95%

“…The results of [4] were extended in [7] to the case of linear neutral type systems with several delays:…”

mentioning

confidence: 99%

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Estimates for Solutions of One Class of Nonlinear Neutral Type Systems with Several Delays

Демиденко

Матвеева

2016

J Math Sci

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We consider a class of systems of nonlinear differential equations of neutral type with several delays. We obtain conditions of exponential stability of the zero solution and establish estimates characterizing the exponential decay rate of solutions at infinity. Bibliography: 14 titles.We consider systems of differential equations with several delays of the formwhere D, A, and B j are constant n × n-matrices, τ j > 0 are the delay parameters, τ 1 > τ k , . . . , m, and F (t, u, v 1 , . . . , v m ) is a real-valued continuous vector-valued function satisfying the Lipschitz condition with respect to u and the inequalityIn the case D = 0, systems of the form (1) are referred to as neutral type systems [1].

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