• Journal of Korea Society of Industrial Information Systems
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• v.12 no.5
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• pp.54-59
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• 2007

We abtain some stability results for a very general differential system using the method of cone valued vector Lyapunov functions and conversely some sufficient conditions for existence of such vector Lyapunov functions.

• Journal of Industrial Technology
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• v.11
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• pp.33-41
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• 1991

Using the Brayton and Tong's computer-generated Lyapunov functions, we stabilize the multilocomotive train system so that the system is globally asymptotically stable. We decompose an interconnected system into the second order subsystems. Lyapunov functions of the free subystems are constructed using the Brayton and Tong's algorithm. An aggregated test matrix is determined in terms of the qualitative properties of the free subsystems and the interconnecting structures. Stated feedback is used for stabilizing the entire system.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.1-11
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• 2014

In this paper, we show that general nonlinear switched systems are asymptotically controllable if and only if there exist control-Lyapunov functions for their relaxation systems. If the switching signal is dependent on the time, then the control-Lyapunov functions are continuous. And if the switching signal is dependent on the state, then the control-Lyapunov functions are $C^1$-smooth. We obtain the results from the viewpoint of control system theory. Our approach is based on the relaxation theorems of differential inclusions and the classic Lyapunov characterization.

• Proceedings of the KIEE Conference
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• 2003.11b
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• pp.131-134
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• 2003

In this paper, we consider the problem of finding the stability region in state space for uncertain linear systems with input saturation. For stability analysis, two Lyapunov functions are chosen. One is for the lineal region and the other is for the saturated legion. Piecewise Lyapunov functions are obtained by solving successive linear matrix inequalites(LMIs) relaxations. A sufficient condition for robust stability is derived in the form of stability region of initial conditions. A numerical example shows the effectiveness of the proposed method.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.345-352
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• 2007

In this paper, cone-valued Lyapunov functions are employed to study the impulsive control system with variable times. The stability criteria on the non-zero solution of the impulsive control system are given by the cone-valued Lyapunov functions and the results of the controllability on the control system are also obtained.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.883-893
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• 2011

In this paper we study h-stability of the solutions of nonlinear difference system via the notion of $n_{\infty}$-summable similarity between its variational systems. Also, we show that two concepts of h-stability and h-stability in variation for nonlinear difference systems are equivalent. Furthermore, we characterize h-stability for nonlinear difference systems by using Lyapunov functions.

• Proceedings of the KIEE Conference
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• 1995.11a
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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.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.155-158
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• 1997

In this paper, we present new results concerning the relationship between the input-output and Lyapunov stability of nonlinear system possessing a periodic orbit. Definition of small-signal finite-gain L$\sub$p/ stability around periodic orbit is introduced. We show L$\sub$p/ stability of exponentially stable periodic orbit using quadratic Lyapunov functions for the periodic orbit. The L$\sub$2/ gain analysis is presented with Hamiltonian-Jacobi inequality along with an example.

• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.1
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• pp.46-51
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• 1987

Using the computer-generated Lyapunov functions due to Brayton-tong's constructive algorithm, we estimate the domains of attraction of dynamical systems of the second order, and analyze the asymptotic stability of large scale contincous-time and discrete-time systems by the decomposition and aggregation method. With this approach we get the less conservative stability results than the existing methods.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.127-133
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• 2012

In this paper we give a necessary and sufficient condition for characterizing $h$-stability for linear dynamic systems on time scales by using Lyapunov functions.