Stability investigation of nonlinear quadratic discrete dynamics systems in the critical case

Diblı́k, Josef; Khusainov, D. Ya.; Grytsay, Irina

doi:10.1088/1742-6596/96/1/012042

Cited by 5 publications

(1 citation statement)

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“…During the last decades, the stability analysis of switched linear continuous/discrete time-delay systems has attracted a lot of attention [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The main approach for stability analysis relies on the use of Lyapunov-Krasovskii functionals and linear matrix inequlity (LMI) approach for constructing a common Lyapunov function [19][20][21][22][23][24]. Although many important results have been obtained for switched linear continuoustime systems, there are few results concerning the stability of switched linear discrete systems with time-varying delays.…”

Section: Introductionmentioning

confidence: 99%

New sufficient conditions for the asymptotic stability of discrete time-delay systems

Sangapate

2012

Adv Differ Equ

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This paper is concerned with asymptotic stability of switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the asymptotic stability for the system is designed via linear matrix inequalities. Numerical example is included to illustrate the effectiveness of the result.

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Section: Introductionmentioning

confidence: 99%

New sufficient conditions for the asymptotic stability of discrete time-delay systems

Sangapate

2012

Adv Differ Equ

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Asymptotic behavior of solutions of nonlinear discrete systems in critical cases

Grushkovskaya

2024

Nonlinear Dyn

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The paper is dedicated to the analysis of the asymptotic behavior of essentially nonlinear discrete systems whose linearization possesses eigenvalues on the unit circle. For these systems, the paper establishes sufficient conditions for the asymptotic stability regardless of terms higher than the third order. Moreover, it derives an asymptotic stability criterium for a reduced critical subsystem. The proof incorporates a constructive approach for deriving Lyapunov functions using the center manifold reduction and normal form method. The key result of the paper asserts that, given the obtained stability conditions, the solutions of the system converge to the origin with a polynomial decay rate. The paper also introduces a method for evaluating the coefficients of the decay rate estimate. To illustrate these findings, we apply the obtained result to analyzing nonlinear business cycle and predator-pray models.

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Boundedness and Stability for Discrete‐Time Delayed Neural Network with Complex‐Valued Linear Threshold Neurons

Duan

Song

2010

Discrete Dynamics in Nature and Society

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The discrete-time delayed neural network with complex-valued linear threshold neurons is considered. By constructing appropriate Lyapunov-Krasovskii functionals and employing linear matrix inequality technique and analysis method, several new delay-dependent criteria for checking the boundedness and global exponential stability are established. Illustrated examples are also given to show the effectiveness and less conservatism of the proposed criteria.

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Stability investigation of nonlinear quadratic discrete dynamics systems in the critical case

Cited by 5 publications

References 1 publication

New sufficient conditions for the asymptotic stability of discrete time-delay systems

New sufficient conditions for the asymptotic stability of discrete time-delay systems

Asymptotic behavior of solutions of nonlinear discrete systems in critical cases

Boundedness and Stability for Discrete‐Time Delayed Neural Network with Complex‐Valued Linear Threshold Neurons

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