New criteria for exponential stability of nonlinear difference systems with time-varying delay

Ngoc, Pham Huu Anh; Hieu, Le Trung

doi:10.1080/00207179.2013.792004

Cited by 26 publications

(25 citation statements)

References 10 publications

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“…As noted above, the results of the recent paper [9] are not applicable to Example 5 or 6. We will explain this using Example 6.…”

Section: Remarkmentioning

confidence: 85%

“…The results are also independent of those in other sources mentioned in the list of references. For example, some new criteria for exponential stability of nonlinear difference systems with time-varying delay were recently proved in [9] where nonlinearities are estimated by linear terms whose matrices are nonnegative and their sum can, for example, be estimated by a constant nonnegative matrix with a spectrum less than 1. For more details, we refer to [9, Theorem 2.2].…”

Section: A Discussion Of the Results Obtained Comparisons And Examplesmentioning

confidence: 99%

“…We will explain this using Example 6. To apply, for example, Theorem 2.3 in [9] we develop the best possible estimations of the right-hand sides of (51) (below, the notation of the above-mentioned paper is used). We get …”

Section: Remarkmentioning

confidence: 99%

“…Recently, growing interest has been paid to investigating the stability of linear difference systems with delay (see, e.g., [1][2][3][4][5][6][7][8][9][10][11]). …”

Section: Introductionmentioning

confidence: 99%

“…The right-hand side inequality in (12) is an obvious consequence of (8) and (9). Let us consider the expression in the square brackets in (11).…”

mentioning

confidence: 99%

See 4 more Smart Citations

Exponential Stability of Linear Discrete Systems with Variable Delays via Lyapunov Second Method

Diblı́k

2017

Discrete Dynamics in Nature and Society

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The paper investigates the exponential stability of a linear system of difference equations with variable delays ( + 1) = ( ) + ∑ =1 ( ) ( − ( )), = 0, 1, . . ., where ∈ N, is a constant square matrix, ( ) are square matrices, ( ) ∈ N ∪ {0}, and ( ) ≤ for an ∈ N. New criteria for exponential stability are derived using the method of Lyapunov functions and formulated in terms of the norms of matrices of linear terms and matrices solving an auxiliary Lyapunov equation. An exponential-type estimate of the norm of solutions is given as well. The efficiency of the derived criteria is numerically demonstrated by examples and their relations to the well-known results are discussed.

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“…As noted above, the results of the recent paper [9] are not applicable to Example 5 or 6. We will explain this using Example 6.…”

Section: Remarkmentioning

confidence: 85%

Section: A Discussion Of the Results Obtained Comparisons And Examplesmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

“…Recently, growing interest has been paid to investigating the stability of linear difference systems with delay (see, e.g., [1][2][3][4][5][6][7][8][9][10][11]). …”

Section: Introductionmentioning

confidence: 99%

“…The right-hand side inequality in (12) is an obvious consequence of (8) and (9). Let us consider the expression in the square brackets in (11).…”

mentioning

confidence: 99%

See 3 more Smart Citations

Exponential Stability of Linear Discrete Systems with Variable Delays via Lyapunov Second Method

Diblı́k

2017

Discrete Dynamics in Nature and Society

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On exponential stability of nonlinear Volterra difference equations in phase spaces

Ngoc

Hieu

2014

Math. Nachr.

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Using a novel approach, we present some new explicit criteria for global exponential stability of the zero solution of general nonlinear Volterra difference equations in phase spaces. In particular, this gives a solution to an open problem posed very recently by E. Braverman and I. M. Karabash in Journal of Difference Equations and Applications 18, 909–939 (2012). As an application, we apply the obtained results to study asymptotic behavior of equilibriums of discrete time neural networks.

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On contraction of nonlinear difference equations with time‐varying delays

Ngoc

Trinh

Hieu

et al. 2018

Mathematische Nachrichten

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General nonlinear difference equations with time‐varying delays are considered. Explicit criteria for contraction of such equations are presented. Then some simple sufficient conditions for global exponential stability of equilibria and for stability of invariant sets are derived. Furthermore, explicit criteria for existence, uniqueness and global exponential stability of periodic solutions are derived. Finally, the obtained results are applied to time‐varying discrete‐time neural networks with delay.

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New criteria for exponential stability of nonlinear difference systems with time-varying delay

Cited by 26 publications

References 10 publications

Exponential Stability of Linear Discrete Systems with Variable Delays via Lyapunov Second Method

Exponential Stability of Linear Discrete Systems with Variable Delays via Lyapunov Second Method

On exponential stability of nonlinear Volterra difference equations in phase spaces

On contraction of nonlinear difference equations with time‐varying delays

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