• International Journal of Fuzzy Logic and Intelligent Systems
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• 제12권3호
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• pp.187-192
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• 2012

This paper is concerned with stabilization problem of continuous-time Takagi-Sugeno fuzzy systems. To do this, the stabilization problem is investigated based on the new fuzzy Lyapunov functions (NFLFs). The NFLFs depend on not only the fuzzy weighting functions but also their first-time derivatives. The stabilization conditions are derived in terms of linear matrix inequalities (LMIs) which can be solved easily by the Matlab LMI Toolbox. Simulation examples are given to illustrate the effectiveness of this method.

• 대한수학회지
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• 제37권5호
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• pp.805-821
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• 2000

The paper deals with asymtotic stabillity of nonlinear nonautinomous systems by Lyapunov's direct method. The proposed Lyapunov-like function V(t, x) needs not be continuous in t and Lipschitz in x in a Banach space. The class of systems considered is allowed to be nonautonomous and infinite-dimensional and we relax the boundedness, the Lipschitz assumption on the system and the definite decrescent condition on the Lyapunov function.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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• pp.499-499
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• 2000

The robust stability problems for nominally linear system with nonlinear, structured perturbations arc considered with Lyapunov direct method. The Lyapunov direct method has been utilized to determine the bounds for nonlinear, time-dependent functions which can be tolerated by a stable nominal system. In most cases quadratic forms are used either as components of vector Lyapunov function or as a function itself. The resulting estimates are usually conservative. As it is known, often the conservatism of the bounds we propose to use a piecewise quadratic Lyapunov function. An example demonstrates application of the proposed method.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1994년도 Proceedings of the Korea Automatic Control Conference, 9th (KACC) ; Taejeon, Korea; 17-20 Oct. 1994
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• pp.518-521
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• 1994

Most of the theorems of nonlinear stability is based on the Lyapunov stability theory. The Lyapunov function method is most well-known and provides precise and rigorous theoretical backgrounds. However, the conventional approach to direct stability analysis has been performed without taking account of damping effects. For accurate stability analysis of nonlinear systems, the damping effects should be considered. This paper presents a new method to derive a group of Lyapunov functions to reflect the damping effects by considering the integral relationships of the system governing equations.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2005년도 학술대회 논문집 정보 및 제어부문
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• pp.20-22
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• 2005

In this paper, we propose a novel stability criterion for switched linear systems. The proposed method employs the results on the upper bound of the solution of LME(Lyapunov Matrix Equation) and on the stability of hybrid system. The former guarantees the existence of Lyapunov-like energy functions and the latter shows that the stability of switched linear systems by using these energy functions. The proposed criterion releases the restriction on the stability of switched linear systems comparing with the existing methods and provides us with easy implementation way for pole assignment.

• Journal of Electrical Engineering and information Science
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• 제3권3호
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• pp.322-329
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• 1998

Stability analysis of nonlinear systems is mostly based on the Lyapunov stability theory. The well-known Lyapunov function method provides precise and rigorous theoretical backgrounds. However, the conventional approach to direct stability analysis has been performed without taking account of damping effects, which is pointed as a minor but crucial drawback. For accurate has been performed without taking account of damping effects, which is pointed as a minor but crucial drawback. For accurate stability analysis of nonlinear systems, it is required to take the damping effects into account. This paper presents a new method to derive a group of Lyapunov functions to reflect the damping effects by considering the integral relationships of the system governing equations. A systematical approach is developed to convert a part of damping loss into some appropriate system energy terms. Examples show that the proposed method remarkably improves the estimation of the region of attraction compared considering damping effects. The proposed method can be utilized as a useful tol to determine the region of attraction.

• 전자공학회논문지 IE
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• 제44권4호
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• pp.26-29
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• 2007

본 논문에서는 섭동 시스템 행렬을 가지는 선형 시스템에 대하여 Lyapunov 방정식과 함수를 고려하여 섭동 유계를 유도한다. 그리고 Lyapunov 함수의 도함수가 음의 정의로 보장되는 가장 큰 섭동 구간을 허락하는 Lyapunov 함수의 선택에 대하여 고려한다. 행렬 계수를 가지는 행렬 리카티 방정식의 해 존재에 대하여 살펴보며, 예를 통하여 검증한다.

• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.251-266
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• 2004

We consider a controlled nonlinear mechanical system described by the Lagrange equations. We determine the control forces $Q_1$ and the restrictions for the perturbations $Q_2$ acting on the mechanical system which allow to guarantee the asymptotic stability of the program motion of the system. We solve the problem of stabilization by the direct Lyapunov's method and the method of limiting functions and systems. In this case we can use the Lyapunov's functions having nonpositive derivatives. The following examples are considered: stabilization of program motions of mathematical pendulum with moving point of suspension and stabilization of program motions of rigid body with fixed point.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2004년도 심포지엄 논문집 정보 및 제어부문
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• pp.13-15
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• 2004

In this paper, we propose a novel stability criterion and a guideline of controller design for switched linear systems. Unlike existing criterions such as Lie algebraic method and multiple Lyapunov functions method, the proposed criterion can be applied to each individual system without considering an overall system. By applying the proposed criterion to each individual system separately, a state feedback controller can be easily designed. Stability of the overall system is proved by developing a rule to determine non-increasing Lyapunov functions recursively at each switching instant. An illustrative example is given.

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.125-137
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• 2000

A solution of the findpath problem in which a moving object in required to avoid moving obstacles and move to the designated target in the plane is porcided via the second method of Lyapunov. This paper presents an new control designed by a family of piecewise Lyapunov functions to solve a findpath problem and gives some simultion results of that.