• 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 Journal of the Acoustical Society of Korea
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• v.16 no.4
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• pp.42-48
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• 1997

This paper has apparaised ability of speaker recognition and speech recognition using correlation dimension and Lyapunov dimension. In this method, speech was regarded the cahos that the random signal is appeared in determinisitic raising system. we deduced exact correlation dimension and Lyapunov dimension with searching important orbit from AR model power spectrum when reconstruct strange attractor using Taken's embedding theory. We considered a usefulness of speech recognition and speaker recognition using correlation dimension and Lyapunov dimension that characterized reconstruction attractor. As a result of consideration, which were of use more the speaker recognition than speech recognition, and in case of speaker recognition using Lyapunov dimension were much recognition rate more than speaker recognitions using correlation dimension.

• KIEE International Transaction on Systems and Control
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• v.2D no.2
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• pp.92-96
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• 2002

This paper is concerned with properties of a Lyapunov functional of state delay systems. It is shown that if a state delay system has a pure imaginary pole for some state delay, then no Lyapunov functional satisfying a Lyapunov condition exists periodically with respect to change of the state delay. This periodic property is unique in state delay systems and has been well known in the frequency domain stability conditions. However, in the time domain stability conditions using a Lyapunov functional, the periodic property is not known explicitly.

• 전자공학회논문지 IE
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• v.44 no.4
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• pp.26-29
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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 matrix Riccati equation.

• Journal of the Korean Institute of Telematics and Electronics T
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• v.36T no.4
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• pp.30-37
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• 1999

This study suggested the Fuzzy Lyapunov dimension. The Fuzzy Lyapunov dimension is to evaluate the quantitative variation of the attractor. In this paper the speaker recognition is evaluated by the Fuzzy Lyapunov dimension. It has been proved that the suggested Fuzzy Lyapunov dimension is superior in the discrimination characteristics between standard reference pattern attractors, and in reference to the test pattern attractor, it has been verified that it is the speaker recognition parameter which absorbs the pattern variation. In order to evaluate the Fuzzy Lyapunov dimension as speaker recognition parameter, the mistaken recognition according to discrimination error in each of speaker and standard reference pattern was estimated, and the validity of the speaker recognition parameter was experimental. As the result of the speaker recognition experiment, 97.0[%] of recognition ratio was obtained, and it was confirmed that the Fuzzy Lyapunov dimension was fit for the speaker recognition parameter.

• 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.

• Proceedings of the KIEE Conference
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• 2004.07d
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• pp.2212-2214
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• 2004

Robust stable analysis with the system bounded parameteric variation is very important among the various control theory. This study is to investigate the robust stable conditions using the quadratic form Lyapunov function in which the coefficient matrix is affined linear system. The quadratic stability using the quadratic form Lyapunov function is not investigated yet. The Lyapunov unction is robust stable not to be dependent by the variable parameters, which means that the Lyapunov function is conservative. We suggest the robust stable conditions in the Lyapunov function in which the variable parameters are dependent in order to reduce the conservativeness of quadratic stability.

• 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.