• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.657-664
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• 2000

A new concept of stability that includes Lyapunov and orbital stabilities and leads to concepts in between them is discussed in terms of a given topology of the function space. The criteria for such new concepts to hold are investigted employing suitably Lyapunov-like functions and the comparison principle.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.12
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• pp.2284-2291
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• 2010

In this paper, improved stability criteria for linear systems with time-varying delays are proposed. By constructing a new Lyapunov functional, novel stability criteria are established in terms of linear matrix inequalities (LMIs). Two numerical examples are carried out to support the effectiveness of the proposed method.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.11
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• pp.2119-2130
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• 2011

This paper proposes new delay-dependent robust stability criteria for neural networks with time-varying delays. By construction of a suitable Lyapunov-Krasovskii's (L-K) functional and use of Finsler's lemma, new stability criteria for the networks are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed methods.

• Journal of Electrical Engineering and Technology
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• v.6 no.5
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• pp.713-722
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• 2011

In the present paper, the problem of stability analysis for linear systems with interval time-varying delays is considered. By introducing a new Lyapunov-Krasovskii functional, new stability criteria are derived in terms of linear matrix inequalities (LMIs). Two numerical examples are given to show the superiority of the proposed method.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.11
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• pp.2261-2265
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• 2009

In this paper, the problem of delay-dependent stability of uncertain stochastic systems with time-varying delay is considered. The uncertainties are assumed to be norm-bounded. Based on the Lyapunov stability theory, new delay-dependent stability criteria for the system are derived in terms of LMI(linear matrix inequality). Two numerical examples are given to show the effectiveness of proposed method.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.459-459
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• 2000

The purpose of this paper is the application of the techniques for the new estimation of robustness for the aircraft systems having structured uncertainties. The basic ideas to analyze the system which is the originally nonlinear is Lyapunov direct theorems. The nonlinear systems have various forms of terms inside the system equations and this investigation is confined in the form of bounded uncertainties. The number of uncertainties will be the degree of freedoms in the calculation of the robust stability regions called the robustness bounds. This proposition adopts the theoretical analysis of the Lyapunov direct methods, that is, the sign properties of the Lyapunov function derivative integrated along finite intervals of time, in place of the original method of the sign properties of the time derivative of the Lyapunov function itself. This is the new sufficient criteria to relax the stability condition and is used to generate techniques for the robust design of control systems with structured perturbations. Using this relaxing stability conditions, in this paper, the quadratic form of Lyapunov function is utilized. In this paper, the practical system of vertical take-off and landing (VTOL) aircraft is analyzed with the proposed stability criteria based upon the Lyapunov direct method. The application of numerical procedures can prove the improvements in estimations of robustness with structured uncertainties. The applicable aircraft system is assumed to be linear with time-varying with nonlinear bounded perturbations.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.345-352
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• 2007

In this paper, cone-valued Lyapunov functions are employed to study the impulsive control system with variable times. The stability criteria on the non-zero solution of the impulsive control system are given by the cone-valued Lyapunov functions and the results of the controllability on the control system are also obtained.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.223-240
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• 2011

In this paper, the problem on periodic solutions of the bidirectional associative memory neural networks with both periodic coefficients and periodic time-varying delays is discussed. By using degree theory, inequality technique and Lyapunov functional, we establish the existence, uniqueness, and global asymptotic stability of a periodic solution. The obtained results of stability are less restrictive than previously known criteria, and the hypotheses for the boundedness and monotonicity on the activation functions are removed.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.12
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• pp.121-128
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• 2000

The scope of this paper is focused to the systems which have the time period and they should be necessarily studied in the sense of stability and design method of controller to stabilize the orignal unstable systems. In general, the time periodic systems or the systems having same motions during certain time interval are easily found in rotating motion device, i.e., satellite or helicopter and widely used in factory automation systems. The characteristics of the selected dynamic systems are analyzed with the new stability concept and stabilization control method based on Lyapunov direct method. The new method from Lyapunov stability criteria which satisfies the energy convergence is studied with linear algebraic method. And the numerical procedures are developed with computational programming method to apply to the practical linear periodic systems. The results from this paper demonstrate the usefulness in analysis of the asymptotic stability and stabilization of the unstable linear periodic system by using the developed simulation procedures.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.11
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• pp.2066-2073
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• 2008

In this paper, the problem of global asymptotic stability of uncertain stochastic neural networks with delay is considered. The delay is assumed to be time-varying and belong to a given interval. Based on the Lyapunov stability theory, new delay-dependent stability criteria for the system is derived in terms of LMI(linear matrix inequality). Three numerical examples are given to show the effectiveness of proposed method.