• The Pure and Applied Mathematics
• /
• v.21 no.1
• /
• pp.11-21
• /
• 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
• /
• v.24 no.4
• /
• pp.883-893
• /
• 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.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.39 no.9
• /
• pp.805-815
• /
• 2011

Nonlinear Parabolized Stability Equations(NSPE) can be effectively used to study more throughly the transition process. NPSE can efficiently analyze the stability of a nonlinear region in transition process with low computational cost compared to Direct Numerical Simulation(DNS). In this study, NPSE in general coordinate system is formulated and a computer code to solve numerically the equations is developed. Benchmark problems for incompressible and compressible boundary layers over a flat plate are analyzed to validate the present code. It is confirmed that the NPSE methodology constructed in this study is an efficient and effective tool for nonlinear stability analysis.

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

• Bulletin of the Korean Mathematical Society
• /
• v.40 no.2
• /
• pp.243-251
• /
• 2003

This note Presents sufficient conditions for Lyapunov's stability and instability of a class of nonlinear nonautonomous second-order ordinary differential equations. Such a class includes as particular cases a remarkably large number of differential equations with specific physical applications. Two successive nonlinear transformations are applied to the original differential equation in order to convert it into a more convenient form for stability analysis purposes. The obtained stability / instability conditions depend closely on the parameterization of the original differential equation.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.1
• /
• pp.105-112
• /
• 2011

In this paper, we investigate h-stability of the nonlinear perturbed difference system by using comparison principle.

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

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

• Journal of the Korean Data and Information Science Society
• /
• v.21 no.3
• /
• pp.597-603
• /
• 2010

We obtain, in using generalized norms, some stability results for a very general system of di erential equations using the method of cone-valued Lyapunov funtions and we obtain necessary and/or sufficient conditions for the uniformly asymptotic stability of the nonlinear differential system.

• 제어로봇시스템학회:학술대회논문집
• /
• 1997.10a
• /
• pp.692-695
• /
• 1997

Nonlinear robust attitude controller for 3-axis stabilized spacecraft is designed. Robust stability analysis for nonlinear spacecraft system with disturbance is conducted. External disturbances and parametric uncertainties decrease Spacecraft's attitude pointing accuracy. Sliding Mode Control(SMC) provides stability of system in the face of these disturbances and uncertainties. The concept of quadratic boundedness and quadratic stability are applied to the robust analysis for the nonlinear spacecraft system subject to bounded disturbance torques. Numerical simulation is conducted to compare the analysis result and actual nonlinear simulation. The simulation show that analysis result is valid.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.1
• /
• pp.197-211
• /
• 2013

We study some stability properties in discrete Volterra equations by employing to change Yoshizawa's results in [13] for the nonlinear equations into results for the nonlinear discrete Volterra equations with unbounded delay.