• 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.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2007년도 하계종합학술대회 논문집
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• pp.485-486
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• 2007

In this paper, we use Lyapunov equations and functions to consider the linear systems with perturbed system matrices. And we consider that what choice of Lyapunov function V would allow the largest perturbation and still guarantee that V is negative definite. We find that this is determined by testing for the existence of solutions to a related quadratic equation with matrix coefficients and unknowns the so-called matrix Riccati equation.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1985년도 하계학술회의논문집
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• pp.89-91
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• 1985

• 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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• 제26권4호
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• pp.869-878
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• 2013

We study boundedness of solutions of dynamic equations on time scales by using Lyapunov-type functions.

• 대한전자공학회논문지
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• 제16권5호
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• pp.18-26
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• 1979

본 논문에서는 algebraic matrix Lyapunov equations과 a1gebraic matrix Riccati equations에 관하여 잘 알려져 있는 중요한 결과를 확장한다. 본 연구는 Matrix 미분 방정식에서 양단 경계조건이 존재하는 문제를 다루며 여기에서 얻어지는 결과는 기존하고 있는 결과를 포함하게 된다. 특히 선형 시스템이 periodic feedback gain control로 안정화되는 필요충분조건을 구하며, two-point boundary Riccati equations의 해를 쉽게 구하는 반복 계산방법을 제시한다. 또한 interalwise reeceding horizon을 이용한 새로운 periodic feedback gain control이 시스템을 안전화시켜줌을 보여준다.

• Transactions on Control, Automation and Systems Engineering
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• 제4권2호
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• pp.169-175
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• 2002

A sliding mode control of spacecraft attitude tracking with actuator, especially reaction wheel, is presented. The sliding mode controller is derived based on quaternion parameterization for the kinematic equations of motion. The reaction wheel dynamic equations represented by wheel input voltage are presented. The input voltage to wheel is calculated from the sliding mode controller and reaction wheel dynamics. The global asymptotic stability is shown using a Lyapunov analysis. In addition the robustness analysis is performed for nonlinear system with parameter variations and disturbances. It is shown that the controller ensures control objectives for the spacecraft with reaction wheels.

• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.741-748
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• 2012

In this work, we prove the instability of solutions for a class of nonlinear functional differential equations of the eighth order with n-deviating arguments. We employ the functional Lyapunov approach and the Krasovskii criteria to prove the main results. The obtained results extend some existing results in the literature.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.261-272
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• 2005

In this paper, boundedness criteria are established for solutions of a class of impulsive functional differential equations with infinite delays of the form $x'(t) = F(t, x(\cdot)), t > t^{\ast} {\Delta}x(t_{k})= I(t_{k}, x(t_{k}^{-})), k = 1,2,...$ By using Lyapunov functions and Razumikhin technique, some new Razumikhin-type theorems on boundedness are obtained.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1995년도 추계학술대회 논문집 학회본부
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• pp.195-198
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• 1995

Most of the theorems of nonlinear stability is based on the Lyapunov stability theory. The Lyapunov function method is the most well-known and provides precise and rigorous theoretical backgrounds. However, tile conventional approach to direct stability analysis has been performed without taking account of damping effects. For accurate stability analysis of nonlinear systems, it is required to consider the damping effects. 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. This method tan be utilized as a powerful tool to determine the region of attraction.