• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.311-320
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• 2007

We obtain a discrete analogue of Nohel's result in [5] about asymptotic equivalence between perturbed Volterra system and unperturbed system.

• The Journal of the Acoustical Society of Korea
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• v.15 no.1
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• pp.23-33
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• 1996

In this paper we point out that if the classical principal domain for bispectra is utilized to determine a second-order Volterra model's output, such and output will be incomplete. This deficiency is associated with the periodic nature of the DFT. For this reason, the objective of this paper is to present an "extended" principal domain for Volterra kernels which leads to an improved estimate of the nonlinear system's response. In order to define the extended principal domain, we derive a new discrete frequency-domain Volterra model from a discrete time-domain Volterra model utilizing 2-dimensional DFT and the relationship between the quadratic component of the Volterra model and a square filter. The effect of the extended domain on the model output is interpreted in terms of the periodicity of DFT. Through computer simulations, we demonstrate the effects of the extended principal domain on the Volterra modeling. The simulation results indicate that the extended principal domain plays and important role in computing Volterra model outputs and estimating Volterra model coefficients.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.535-543
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• 2009

We investigate h-stability of solutions of nonlinear Volterra difference systems and linear Volterra difference systems.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.161-164
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• 1996

The authors have recently proposed a new method for identifying Volterra kernels of nonlinear control systems by use of M-sequence and correlation technique. A specially chosen M-sequence is added to the nonlinear system to be identified, and the crosscorrelation function between the input and output is calculated. Then every crosssection of Volterra kernels up to 3rd order appears at a specified delay time point in the crosscorrelation. This method is applied to a saturation-type nonlinear feedback control system of mechanical-electrical servo system having torque saturation nonlinearity. Simulation experiments show that we can obtain Volterra kernels of saturation-type nonlinear system, and a good agreement is observed between the observed output and the calculated one from the measured Volterra kernels.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.280-284
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• 1998

Many classes of nonlinear systems can be represented by Volterra kernel expansion. Therefore, identification of Volterra kernels of nonlinear system is an important task for obtaining the nonlinear characteristics of the nonlinear system. Although one of the authors has recently proposed a new method for obtaining the Volterra kernels of a nonlinear system by use of M-sequence and correlation technique, our mettled of nonlinear system identification is limited to Wiener-type nonlinear system and we can not apply this method to the identification of Hammerstein-type nonlinear system. This paper describes a new mettled for obtaining Volterra kernels of Hammerstein nonlinear system by adding a linear element in front of tile Hammerstein system. First we calculate the linear element of Hammerstein system by use of conventional correlation method. Secondly, we put a linear element in front of Hammerstein system. Then the total system becomes Wiener-type nonlinear system. Therefore we can use our method on Volterra kernel identification by use of M-sequence. Thus we get the coefficients of the approximation polynomial of nonlinear element of Hammerstein system. From the results of simulation, a good agreement with theoretical considerations is obtained, showing a wide applicability of our method.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.407-416
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• 1999

In this paper we give some sufficient conditions for the existence and uniqueness of a continuous for the existence and uniqueness of a continuous slution of the system of Urysohn-Volterra equation with hysteresis.

• 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.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.597-600
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• 1997

In this paper, the authors propose a new method for linearizing a nonlinear dynamical system by use of polynomial compensation. In this method, an M-sequence is applied to the nonlinear system and the crosscorrelation function between the input and the output gives us every crosssections of Volterra kernels of the nonlinear system up to 3rd order. We construct a polynomial compensation function from comparison between lst order Volterra kernel and high order kernels. The polynomial compensation function is, in this case, of third order whose coefficients are variable depending on the amplitude of the input signal. Once we can get compensation function of nonlinear system, we can construct a linearization scheme of the nonlinear system. That is. the effect of second and third order Volterra kernels are subtracted from the output, thus we obtain a sort of linearized output. The authors applied this method to a saturation-type nonlinear system by simulation, and the results show good agreement with the theoretical considerations.

• Proceedings of the KIEE Conference
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• 2004.05a
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• pp.3-6
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• 2004

In this paper, the problem of identifying a time-varying nonlinear system in an adaptive way was considered, whereby the time-varying second-order Volterra series was employed to model the system and the filtered weighted least squares (FWLS) algorithm was utilized for the fast parameter tracking capability with low computational burden. Finally, the performance of the proposed approach was demonstrated by providing some computer simulation results.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.3
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• pp.139-151
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• 2008

We investigate a three species food chain system with Lotka-Volterra type functional response and impulsive perturbations. We find a condition for the local stability of prey or predator free periodic solutions by applying the Floquet theory and the comparison theorems and show the boundedness of this system. Furthermore, we illustrate some examples.