• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권4호
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• pp.329-336
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• 2011

Some new Lyapunov-type inequalities for a class of nonlinear differential systems, which are natural refinements and generalizations of the well-known Lyapunov inequality for linear second order differential equations, are given. The results of this paper cover some previous results on this topic.

• 충청수학회지
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• 제25권3호
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• pp.589-597
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• 2012

In this paper we investigate the stability of solutions of the perturbed differential equations with the positive order of the perturbation by using the notion of the Lyapunov exponent of unperturbed equations and an integral inequality of Bihari type.

• Journal of applied mathematics & informatics
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• 제8권1호
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• pp.297-303
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• 2001

In this paper, the problem of the stability analysis for a class of linear neutral systems with time-varying delay is investigated. Using the Lyapunov method, a delay-dependent sufficient condition for asymptotic stability of the systems in terms of linear matrix inequalities (LMIs) is presented. The LMIs can be easily solved by various convex optimization algorithms.

• Kyungpook Mathematical Journal
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• 제61권1호
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• pp.1-10
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• 2021

This paper is concerned the finite time blow-up of solution for higher-order nonlinear Kirchhoff-type equation with a degenerate term and a source term. By an appropriate Lyapunov inequality, we prove the finite time blow-up of solution for equation (1.1) as a suitable conditions and the initial data satisfying ||Dmu0|| > B-(p+2)/(p-2q), E(0) < E1.

• 대한수학회보
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• 제47권1호
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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.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2011년도 제42회 하계학술대회
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• pp.1732-1733
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• 2011

This paper presents observer-based controller design for interval type-2 fuzzy system with staircase membership approximation. In type-2 fuzzy case, membership function is itself fuzzy set itself. Thus, type-2 fuzzy system can deal with parametric uncertainties of nonlinear system by capturing the uncertainties in membership function. Likewise, stabilization condition of type-2 fuzzy system is derived from quadratic Lyapunov function, and it goes to linear matrix inequality. Furthermore, in this paper, to relax the conservativeness of stabilization condition, staircase membership function approximating method is applied. Observer-based control method is adopted to control system which has some unmeasurable states. To prove suitability of our proposed method, numerical example is presented.

• 전기학회논문지
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• 제66권11호
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• pp.1620-1627
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• 2017

In this paper, we design an observer-based $H_{\infty}$ fuzzy controller for interval type-2 Takagi-Sugeno (T-S) fuzzy systems under imperfect premise matching. The designed observer-based controller can effectively estimate the state of the system and make fuzzy system satisfy the $H_{\infty}$ disturbance attenuation performance. Using the slack matrix, the derived stabilization condition is expressed in terms of a linear matrix inequality. Finally, the effectiveness of the proposed method is verified through a simulation example.

• 한국지능시스템학회논문지
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• 제20권2호
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• pp.159-164
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• 2010

본 논문에서는 뉴트럴 타입 시간 지연을 갖는 네트워크 제어 시스템의 안정도 분석 및 제어기 설계에 대해서 논의한다. 네트워크상에서 발생하는 뉴트럴 타입 시간 지연을 모델링하며, 전체 네트워크 제어 시스템은 뉴트럴 타입 시간 지연을 가지는 비선형 시스템이 된다. 시간 지연 분산 방법을 이용하여 기존과 다른 새로운 안정도 조건을 유도한다. 리아프노푸 함수를 이용하여 제안된 네트워크 제어 시스템을 안정화 시키는 퍼지 제어기 설계를 위한 충분조건을 유도한다. 제안된 충분조건을 선형 행렬 부등식의 형태로 나타내고, 해를 통하여 퍼지 제어기의 이득 값을 설계한다. 예제를 통하여 제안된 이론의 타당성을 확인한다.

• 대한수학회지
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• 제48권4호
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• pp.727-747
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• 2011

By employing coincidence degree theory and using Halanay-type inequality technique, a sufficient condition is given to guarantee the existence and global exponential stability of periodic solutions for the two-dimensional discrete-time Cohen-Grossberg BAM neural networks. Compared with the results in existing papers, in our result on the existence of periodic solution, the boundedness conditions on the activation are replaced with global Lipschitz conditions. In our result on the existence and global exponential stability of periodic solution, the assumptions in existing papers that the value of activation functions at zero is zero are removed.

• 전자공학회논문지
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• 제49권10호
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• pp.181-186
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• 2012

본 논문에서는 변수 불확실성과 필터이득 섭동을 가지는 시스템에 대한 견실비약성 $H_{\infty}$ 칼만형필터 설계기법을 제안한다. 필터가 존재할 충분조건과 견실비약성 $H_{\infty}$ 필터 설계기법을 선형행렬부등식 (LMI: Linear Matrix Inequality 접근법으로 제안하고 시스템과 필터의 불확실성을 매개변수화 선형행렬부등식(PLMI: Parameterized Linear Matrix Inequality)으로 구조화된 불확실성의 형태로 표현한 후 Lyapunov 함수를 통해 시스템의 불확실성과 더불어 필터이득섭동을 고려한 칼만형 $H_{\infty}$ 필터가 존재할 충분조건과 필터설계기법을 PLMI 형태로 보인다. PLMI는 무한개의 LMI의 형태로 나타나므로 완화기법(relaxation technique)을 적용하여 유한개의 LMI의 형태로 변환한 후 견실하고 최적화된 필터이득과 필터섭동범위를 계산하고, 예제와 모의실험을 통해 제시된 필터의 타당성을 검증한다.