• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.04a
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• pp.372-375
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• 2007

본 논문은 시간 변동 시간 지연을 가지는 선형 Neutral 시스템에 관한 관측기 설계에 대해서 논의한다. 시간 지연을 가지는 시스템의 안정도를 판별하기 위하여 Lyapunov-Krasovskii의 이론을 도입한다. 시스템의 안정도를 위한 조건으로 시간 변동 시간 지연에 종속적인 충분조건을 제시한다. 선형 행렬 부등식을 이용하여 관측기의 이득값을 설계하며, 오차 상태 방정식의 안정도를 판별한다. 본 논문의 결과는 Luenberger가 제안한 관측기의 일반적인 결과를 나타낸다. 모의실험을 통해 논문의 결과를 입증하였다.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.255-268
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• 2005

We use Krasnoselskii's fixed point theorem to show that the nonlinear neutral difference equation with delay x(t + 1) = a(t)x(t) + c(t)${\Delta}$x(t - g(t)) + q(t, x(t), x(t - g(t)) has a periodic solution. To apply Krasnoselskii's fixed point theorem, one would need to construct two mappings; one is contraction and the other is compact. Also, by making use of the variation of parameters techniques we are able, using the contraction mapping principle, to show that the periodic solution is unique.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.813-838
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• 2011

In this paper, we prove sufficient conditions for controllability of second order semi-linear neutral impulsive differential inclusions on unbounded domain with infinite delay in Banach spaces using the theory of strongly continuous Cosine families. We shall rely on a fixed point theorem due to Ma for multi-valued maps. The controllability results in infinite dimensional space has been proved without compactness on the family of Cosine operators.

• Journal of Applied and Pure Mathematics
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• v.4 no.3_4
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• pp.107-122
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• 2022

This manuscript aims to investigate the existence, uniqueness, and stability of non-local random impulsive neutral stochastic differential time delay equations (NRINSDEs) with Poisson jumps. First, we prove the existence of mild solutions to this equation using the Banach fixed point theorem. Next, we demonstrate the stability via continuous dependence initial value. Our study extends the work of Wang, and Wu [16] where the time delay is addressed by the prescribed phase space 𝓑 (defined in Section 3). To illustrate the theory, we also provide an example of our methods. Using our results, one could investigate the controllability of random impulsive neutral stochastic differential equations with finite/infinite states. Moreover, one could extend this study to analyze the controllability of fractional-order of NRINSDEs with Poisson jumps as well.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.37 no.6
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• pp.1-6
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• 2000

In this paper, the problem of the stability analysis for linear neutral delay-differential systems with nonlinear perturbations is investigated. Using Lyapunov second method, a new delay-dependent sufficient condition for asymptotic stability of the systems in terms of linear matrix inequalities (LMIs), which can be easily solved by various convex optimization algorithms, is presented. A numerical example is given to illustrate the proposed method.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.2
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• pp.174-179
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• 2009

We consider the stabilization problem for a class of networked control systems with neutral type of time delays. The neutral type of time-delays occur in controller-to-actuator and sensor-to-controller. The Takagi-Sugeno (T-S) fuzzy model is employed to represent a nonlinear system with neutral type of time-delays. The stabilization via state-feedback is first addressed, and delay-range-dependent stabilization conditions are proposed in terms of linear matrix inequalities (LMIs). Finally, an application example will be given to show the merits and design a procedure of the proposed approach.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.4
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• pp.253-265
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• 2011

In this paper, we study the existence of mild solutions for double perturbed impulsive neutral functional evolution equations with infinite delay in Banach spaces. The existence of mild solutions to such equations is obtained by using the theory of the Hausdorff measure of noncompactness and Darbo fixed point theorem, without the compactness assumption on associated evolution system. An example is provided to illustrate the theory.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.127-144
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• 2005

In this paper, we consider the higher order nonlinear neutral delay difference equation of the form $\Delta^{\gamma}(x_{n}+px_{n-\gamma})+f(n, x_{n-\sigma_1(n)}, x_{n-\sigma_2(n)}, \ldots, x_{n-\sigma{_m}(n)})=0$. We give an integrated classification of nonoscillatory solutions of the above equation according to their asymptotic behaviours. Necessary and sufficient conditions for the existence of nonoscillatory solutions with designated asymptotic properties are also established.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.11
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• pp.2023-2026
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• 2007

In this letter, the problem for a class of neutral differential equation is considered. Based on the Lyapunov method, a stability criterion, which is delay-dependent on both ${\tau}\;and\;{\sigma}$, is derived in terms of linear matrix inequality (LMI). Two numerical examples are carried out to support the effectiveness of the proposed method.

• Advances in Computational Design
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• v.9 no.2
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• pp.97-113
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• 2024

In this paper, we proposed a new class of stochastic neutral neural networks with uncertain and deterministic coefficients. Made the Sigmund activation and Lipschitz activation functions less conditional. The Lyapnov-Krasovskii functional is constructed. The linear matrix inequality (LMI) is constructed using Schur's lemma, and new criteria for the global asymptotic stability and global asymptotic robust stability of neural networks are obtained. Furthermore, we have verified that the method is effective and feasible through numerical examples.