• 제어로봇시스템학회:학술대회논문집
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• 1990.10b
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• pp.1060-1065
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• 1990

In general it is difficult to determine a Liapunov function for a given asymptotically stable, nonlinear differential equations system. But, in the system with control inputs, it is feasible to make a given positive function, except for a small area, globally satisfy the conditions of the Liapunov function for the system. We call such a positive function a Liapunov-like function, and propose a method of nonlinear optimal regulator using this Liapunov-like function. We also use the periodic Liapuitov-like friction that suits the system whose equilibrium points exist periodically. The relationship between the Liapunov function and cost function which this nonlinear regulator minimizes is considered using inverse optimal method.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1623-1628
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• 2004

In the 3-dimensional cyclic Lotka-Volterra equations, we show the solution on the invariant hyperplane. In addition, we show the existence of the invariant hyperplane by the center manifold theorem under the some conditions. With this result, we can lead the hyperplane of the n-dimensional cyclic Lotka-Volterra equaions. In other section, we study the 3- or 4-dimensional Hamiltonian Lotka-Volterra equations which satisfy the Jacobi identity. We analyze the solution of the Hamiltonian Lotka- Volterra equations with the functions called the split Liapunov functions by [4], [5] since they provide the Liapunov functions for each region separated by the invariant hyperplane. In the cyclic Lotka-Volterra equations, the role of the Liapunov functions is the same in the odd and even dimension. However, in the Hamiltonian Lotka-Volterra equations, we can show the difference of the role of the Liapunov function between the odd and the even dimension by the numerical calculation. In this paper, we regard the invariant hyperplane as the important item to analyze the motion of Lotka-Volterra equations and occur the chaotic orbit. Furtheremore, an example of the asymptoticaly stable and stable solution of the 3-dimensional cyclic Lotka-Volterra equations, 3- and 4-dimensional Hamiltonian equations are shown.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.2
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• pp.123-131
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• 2006

In this paper, a numerical programming for Liapunov index of differential equations with periodic coefficients depending on parameters is given. The associated equations are given at first, then existence of periodic solutions to the associated equations is proved in this paper. And we compute periodic solution u(t) of the associated equations. Finally, we give the error of approximate calculation.

• Journal of the Korean Mathematical Society
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• v.36 no.4
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• pp.757-771
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• 1999

We consider a system of functional differential equations x'(t)=F(t, $x_t$) and obtain conditions on a Liapunov functional and a Liapunov function to ensure the instability of the zero solution.

• Bulletin of the Korean Mathematical Society
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• v.34 no.3
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• pp.371-383
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• 1997

In recent years M. Pinto introduced the notion of h-stability. He extended the study of exponential stability to a variety of reasonable systems called h-systems. We investigate h-stability for the nonlinear differential systems using the notions of $t_\infty$-similarity and Liapunov functions.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.9 no.2
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• pp.77-84
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• 1984

In this paper, the method of the stability test of the Two-Dimensional digital filters is developed. The Liepunov's stability theorem of One-Dimensional discrete system is extended to Two-Dimensional digital filter transfer function which can be transformed twodimensional state space representation. The results developed above is agreed with of mapping method.

• 제어로봇시스템학회:학술대회논문집
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• 1990.10b
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• pp.1289-1294
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• 1990

When a saturating control system has integral action, reset windup can cause instability as well as make the system performance unsatisfactory. An antirset-windup (ARW) limiter has been suggested to improve the stability and performance. It has been implemented with analog circuits and tested by simulations. This paper presents the stability condition of a double-integrator plant having the state feedback plus integral-action controller with the ARW limiter by using both Liapunov's second method and graphical method together.

• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.135-148
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• 1998

We propose the new controls constructed via the second or direct method of Liapunov to solve the collision avoidance control problems for moving objects and a robot arm in the plane. We also explicate the controlling effect by the simulations.

• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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• pp.69-76
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• 1996

We obtain some properties of reducible differential equations in the sense of Liapunov.

• Proceedings of the KIEE Conference
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• 1977.08a
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• pp.83-89
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• 1977