• Journal of the Korean Data and Information Science Society
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• v.23 no.3
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• pp.595-604
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• 2012

In this article, we consider chaotic behavior happened in nonsmooth dynamical systems. To quantify such a behavior, a computation of Lyapunov exponents for chaotic orbits of a given nonsmooth dynamical system is focused. The Lyapunov exponent is a very important concept in chaotic theory, because this quantity measures the sensitive dependence on initial conditions in dynamical systems. Therefore, Lyapunov exponents can decide whether an orbit is chaos or not. To measure the sensitive dependence on initial conditions for nonsmooth dynamical systems, the calculation of Lyapunov exponent plays a key role, but in a theoretical point of view or based on the definition of Lyapunov exponents, Lyapunov exponents of nonsmooth orbit could not be calculated easily, because the Jacobian derivative at some point in the orbit may not exists. We use an algorithmic calculation method for computing Lyapunov exponents using time series for a two dimensional piecewise smooth dynamic system.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.10
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• pp.1508-1512
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• 2012

This paper presents a relaxed stability condition for continuous-time affine fuzzy system using fuzzy Lyapunov function. In the previous studies, stability conditions for the affine fuzzy system based on quadratic Lyapunov function have a conservativeness. The stability condition is considered by using the fuzzy Lyapunov function, which has membership functions in the traditional Lyapunov function. Based on Lyapunov-stability theory, the stability condition for affine fuzzy system is derived and represented to linear matrix inequalities(LMIs). And slack matrix is added to stability condition for the relaxed stability condition. Finally, simulation example is given to illustrate the merits of the proposed method.

• 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.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.46 no.4
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• pp.49-57
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• 2009

In this paper we consider the specific types of the generalized continuous-time Lyapunov equation and the existence of solution. This is motivated to analyze the system stability in situations where descriptor system has infinite eigenvalue. As main results, firstly the necessary and sufficient condition for stability of the descriptor system with index one or two will be proposed. Secondly, for the general case of any index, the similar condition for stability of descriptor system will be proposed with the specific type of the generalized Lyapunov equation. Finally some examples are used to show the validity of proposed methods.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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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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• 2000.10a
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• pp.12-12
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• 2000

This paper consider a new weighted model reduction using block diagonal solutions of Lyapunov inequalities. With the input and/or output weighting function, the stability of reduced order system is quaranteed and a priori error bound is proposed. to achieve this, after finding the solutions of two Lyapunov inequalities and balancing the full order system, we find the reduced order systems using the direct truncation and the singular perturbation approximation. The proposed method is compared with other existing methods using numerical example.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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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.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.7
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• pp.650-658
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• 2012

This paper proposes a high performance position controller for a driving system using a time optimal controller which has been widely used to control driving systems to achieve desired reference position or velocity in a minimum response time. The main purpose of this research lies in an improvement of transient response performance rather than that of steady-state response in comparison with other control strategies. In order to refine the scheme of time optimal control, Lyapunov stability proofs are incorporated in a controller of standard second order system model. This scheme is applied to the control of a driving system. In view of the simulation and experiment results, the standard second order system model exhibits better minimum-time control performance and robustness than double integral system model does.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.155-163
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• 2002

The purpose of this paper is to establish discrete versions of the well-known Lyapunov's stability theorem and LaSalle's invariance theorem for a non-autonomous discrete dynamical system. Our proofs for these theorems are constructive in the sense that they are made by explicitly building a Lyapunov function for the system. A comparison between non-autonomous discrete dynamical systems and continuous dynamical systems is conducted.