• East Asian mathematical journal
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• v.36 no.5
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• pp.547-554
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• 2020

Synchronization of unidirectional identical FitzHugh-Nagumo systems coupled in a ring structure under ionic and external electrical stimulations is investigated. In this network, each neuron is only connected and transmit signals to its next neuron via synaptic strength called gapjunctions. Adaptive control theory and Lyapunov stability theory are used to propose a unique control scheme with necessary and sufficient conditions which guarantee the synchronization of the neuronal network. Finally, the effectiveness of the proposed scheme is shown through numerical simulations.

• Proceedings of the KIEE Conference
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• 1992.07a
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• pp.377-380
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• 1992

This paper proposes a novel direct adaptive pole placement control algorithm which can be applied to continuous time nonminimum phase systems. The algorithm is based on Lyapunov's direct method. By introducing an auxiliary signal, a minimal error model is constructed in state space. Using the error model an estimation law is obtained via Lyapunov's second stability theorem. The global stability of the overall system is established.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.227-230
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• 1995

Stability of a coupled nonautonomous ordinary differential equation is investigated. Asymptotic convergence to zero of a part of state vector is additionally shown, otherwise only uniform stability could have been concluded by the Lyapunov direct method. Obtained results could be particularly useful in analysis of nonautonomous systems in which the invariance principle does not hold. An illustrating example is given.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.420-423
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• 1995

The stability of system is one of the important aspects and to judge system's stability is another complicated problem. Previously, new technique derived from relaxing Lyapunov conditions has been already introduced and in this paper, this proposed technique applies to the practical dynamic systems. This utility of numerical procedures prove the comparable improvements of the estimation of robustness for dynamic systems having structured (bounded) perturbations.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.103-117
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• 2011

By using an important lemma, some analysis techniques and Lyapunov functional method, we establish the sufficient conditions of the existence of equilibrium solution of a class of BAM neural network with impulses and distributed delays. Finally, applications and an example are given to illustrate the effectiveness of the main results.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.7
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• pp.523-528
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• 2000

In this short note the characteristics of a nonlinear system of which the state trajectories are oscillating in the phase plane are overviewed. The physical concept of stuck and sliding patch phenomena are also introduced by adding some switching functions and their stability on the sliding patches are analyzed by using the Lyapunov stability theory and Frobenius theorem.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.257-279
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• 2023

Applying the Lyapunov-Schmidt reduction, we consider spectral stability of small amplitude stationary periodic solutions bifurcating from an equilibrium of the generalized Swift-Hohenberg equation. We follow the mathematical framework developed in [15, 16, 19, 23] to construct such periodic solutions and to determine regions in the parameter space for which they are stable by investigating the movement of the spectrum near zero as parameters vary.

• Journal of the Korean Institute of Intelligent Systems
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• v.21 no.5
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• pp.630-636
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• 2011

This paper is concerned with the stability analysis and stabilization for the Takagi-Sugeno(T-S) fuzzy systems with parametric uncertainties. To reduce conservativeness in stability analysis for T-S fuzzy systems, fuzzy Lyapunov functions are used. Stability analysis is performed and robust fuzzy controller is designed for stabilization of the system with parametric uncertainties. The stability and stabilization conditions are formulated in terms of linear matrix inequalities (LMIs). Finally, simulation example is presented to show the effectiveness of the proposed approach.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.9
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• pp.1748-1753
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• 2011

In this paper, we consider the stability of linear systems with an interval time-varying delay. It is known that the adoption of decomposition of delay improves the stability result. For the interval time-delay case, they applied it to the interval of time-delay and got less conservative results. Our basic idea is to apply the general decomposition to the low limit of delay as well as interval of time-delay. Based on this idea, by using the modified Lyapunov-Krasovskii functional and newly derived Lemma, we present a less conservative stability criterion expressed as in the form of linear matrix inequality(LMI). Finally, we show, by well-known two examples, that our result is less conservative than the recent results.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.89-102
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• 2010

This paper concerns the problem of global robust stability of a time-delay discontinuous system with a positive-defined connection matrix under polytopic-type uncertainty. In order to give the stability condition, we firstly address the existence of solution and equilibrium point based on the properties of M-matrix, Lyapunov-like approach and the theories of differential equations with discontinuous right-hand side as introduced by Filippov. Second, we give the delay-independent and delay-dependent stability condition in terms of linear matrix inequalities (LMIs), and based on Lyapunov function and the properties of the convex sets. One numerical example demonstrate the validity of the proposed criteria.