• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.883-893
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• 2011

In this paper we study h-stability of the solutions of nonlinear difference system via the notion of $n_{\infty}$-summable similarity between its variational systems. Also, we show that two concepts of h-stability and h-stability in variation for nonlinear difference systems are equivalent. Furthermore, we characterize h-stability for nonlinear difference systems by using Lyapunov functions.

• Transactions on Control, Automation and Systems Engineering
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• v.4 no.1
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• pp.75-77
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• 2002

Stability theorem for nonlinear systems with slowly varying inputs is extended to systems with slowly varying and small jump inputs.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.345-351
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• 2005

An effective method for analyzing the stability of nonlinear systems is developed. After introducing a novel concept named the point- wise generalized Dahlquist constant for any mapping and presenting its useful properties, we show that the point-wise generalized Dahlquist constant is sufficient for characterizing the exponential stability of nonlinear systems.

• The Pure and Applied Mathematics
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• v.21 no.1
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• pp.11-21
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• 2014

The present paper is concerned with the notions of Lipschitz and asymptotic stability for perturbed nonlinear differential system knowing the corresponding stability of nonlinear differential system. We investigate Lipschitz and asymtotic stability for perturbed nonlinear differential systems. The main tool used is integral inequalities of the Bihari-type, in special some consequences of an extension of Bihari's result to Pinto and Pachpatte, and all that sort of things.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.383-389
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• 2010

In this paper, we investigate h-stability of the nonlinear differential systems using the notion of $t_{\infty}$-similarity.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.827-834
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• 2010

In this paper, we investigate h-stability of the nonlinear perturbed differential systems.

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.181-197
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• 2015

In this paper, we investigate Lipschitz and asymptotic stability for perturbed nonlinear differential systems.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.591-602
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• 2014

In this paper, we investigate Lipschitz and asymptotic stability for nonlinear perturbed differential systems.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1555-1565
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• 2013

In this paper, some new generalized discrete Halanay inequalities are established. On the basis of these new established inequalities, we obtain the attracting set and the global asymptotic stability of the nonlinear discrete systems. Our results established here extend the main results in [R. P. Agarwal, Y. H. Kim, and S. K. Sen, New discrete Halanay inequalities: stability of difference equations, Commun. Appl. Anal. 12 (2008), no. 1, 83-90] and [S. Udpin and P. Niamsup, New discrete type inequalities and global stability of nonlinear difference equations, Appl. Math. Lett. 22 (2009), no. 6, 856-859].

• The Pure and Applied Mathematics
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• v.18 no.4
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• pp.337-344
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• 2011

In this paper, we investigate h-stability of the nonlinear perturbed differential systems.