• East Asian mathematical journal
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• v.32 no.3
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• pp.399-412
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• 2016

In this paper, we study the viscoelastic Kirchhoff type equation with the following nonlinear source and time-varying delay $$u_{tt}-M(x,t,{\parallel}{\nabla}u(t){\parallel}^2){\Delta}u+{\int_{0}^{t}}h(t-{\tau})div[a(x){\nabla}u({\tau})]d{\tau}\\+{\parallel}u{\parallel}^{\gamma}u+{\mu}_1u_t(x,t)+{\mu}_2u_t(x,t-s(t))=0.$$ Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the uniform decay rate of the Kirchhoff type energy.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.2
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• pp.376-382
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• 2011

This paper proposes delay-dependent stability conditions of the fuzzy Markovian jumping Hopfield neural networks of neutral type with time-varying delays. By constructing a suitable Lyapunov-Krasovskii's (L-K) functional and utilizing Finsler's lemma, new delay-dependent stability criteria for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. A numerical example is given to illustrate the effectiveness of the proposed methods.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.943-966
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• 2023

In this paper, we study the initial-boundary value problem for viscoelastic wave equations of Kirchhoff type with Balakrishnan-Taylor damping terms in the presence of the infinite memory and external time-varying delay. For a certain class of relaxation functions and certain initial data, we prove that the decay rate of the solution energy is similar to that of relaxation function which is not necessarily of exponential or polynomial type. Also, we show another stability with g satisfying some general growth at infinity.

• Journal of Advanced Navigation Technology
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• v.23 no.6
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• pp.577-583
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• 2019

A dynamic system is called positive if any trajectory of the system starting from non-negative initial states remains forever non-negative for non-negative controls. In this paper, we consider the new stability condition for the positive time-varying linear discrete interval systems with time-varying delay and unstructured uncertainty. The delay time is considered as time-varying within certain interval having minimum and maximum values and the system is subjected to nonlinear unstructured uncertainty which only gives information on uncertainty magnitude. The proposed stability condition is an improvement of the previous results which can be applied only to time-invariant systems or had no consideration of uncertainty, and they can be expressed in the form of a very simple inequality. The stability conditions are derived using the Lyapunov stability theory and have many advantages over previous results using the upper solution bound of the Lyapunov equation. Through numerical example, the proposed stability conditions are proven to be effective and can include the existing results.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.9
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• pp.1796-1801
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• 2009

This paper is concerned with the problem of delay-dependent robust $H_{\infty}$ filtering for uncertain descriptor systems with time-varying delay. The considering uncertainty is convex compact set of polytoic type. The purpose is the design of a linear filter such that the resulting filtering error descriptor system is regular, impulse-free, and asymptotically stable with $H_{\infty}$ norm bound. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent bounded real lemma (BRL) for delayed descriptor systems is derived. Based on the derived BRL, a robust $H_{\infty}$ filter is designed in terms of linear matrix inequaltity (LMI). Numerical examples are given to illustrate the effectiveness of the proposed method.

• Journal of information and communication convergence engineering
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• v.8 no.1
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• pp.103-106
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• 2010

In this paper, the delay times were evaluated to develop highly reliable time-to-digital converter(TDC) in analog and digital delay element structures. The delay element can be designed by using current source or inverter. In case of using inverter, the number of inverter has to be controlled to adjust the delay time. And in case of using current source, the current for charging and discharging is controlled. When the current source is used the delay time of the delay element is not sensitive with varying the channel width of CMOS. However, when the inverter is used the delay time is directly related to the channel width of CMOS. Therefore to obtain good reliability in TDC circuit the delay element using current source is more stable compared to inverter in the viewpoint of the variation of fabrication process.

• Journal of the Korean Society of Safety
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• v.21 no.4 s.76
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• pp.25-32
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• 2006

LonWorks over IP(LonWorks-IP) virtual device network(VDN) is an integrated form of LonWorks device network and IP data network. In especially real-time distributed servo applications on the factory floor, timely response is essential for predictive and preventive maintenance. The time delay in servo control on LonWorks-IP based VDN has highly stochastic nature. LonWorks-IP based VDN induced transmission delay deteriorates the performance and stability of the real-time distributed control system and can't give an effective preventive and predictive maintenance. In order to guarantee the stability and performance of the system, and give an effective preventive and predictive maintenance, LonWorks-IP based VDN induced time-varying uncertain time delay needs to be predicted and compensated. In this paper new Pill control scheme based on Smith predictor, disturbance observer and band pass filter is proposed and tested through computer simulation about position control of DC servo motor. It is shown that how can the proposed control scheme be designed to minimize the effects of uncertain varying time delay and model uncertainties. The validity of the proposed control scheme is compared and demonstrated with the comparison of internal model controllers(IMC) based on Smith predictor with and without disturbance observer.

• Smart Structures and Systems
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• v.21 no.2
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• pp.187-194
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• 2018

This paper focuses on the $H_{\infty}$ filter design problem for offshore steel jacket platforms. Its objective is to design a full-order state observer for offshore platforms in presence of unknown disturbances. To make the method more practical, it is assumed that the measured variables are available at discrete-time instants with time-varying sampling time intervals. By modelling the sampling intervals as a bounded time-varying delay, the estimation error system is expressed as a time-delay system. As a result, the addressed problem can be transformed to the problem of stability of dynamic error between the system and the state estimator. Then, based on the Lyapunov-Krasovskii Functional (LKF), a stability criterion is obtained in the form of Linear Matrix Inequalities (LMIs). According to the stability criterion, a sufficient condition on designing the state estimator gain is obtained. In the end, the proposed method is applied to an offshore platform to show its effectiveness.

• Journal of Drive and Control
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• v.15 no.3
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• pp.21-28
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• 2018

We propose a tension controller based on a time-delay estimation (TDE) technique for a winding machine. Firstly, we perform the necessary calculations to derive a mathematical model of the winding machine. In this sense, it is revealed that the roll radius of the winding machine is characteristically seen to be increasing or decreasing during the winding process. That being said, it is noted that the parameters of the winding machine are coupled and constantly changing during this process. Understandably then, it is noted that the model is shown to be nonlinear and time-varying. Secondly, we propose the way to apply the TDE based controller which is the so-called Time-delay Control (TDC). The TDC utilizes the time-delayed information intentionally to compensate the nonlinear and time-varying characteristics. As we have seen, the proposed controller consists of two parts: one is a TDE component, and the other is an error dynamics component which is defined by a user. In a computer simulation based on the Matlab/Simulink program, the proposed controller is compared with a conventional PID controller, which is widely used in the tension control of the winding machine. The proposed controller reduces the incidence of overshoot and steady-state error in the tension control, as compared to the conventional PID controller.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.42 no.4 s.304
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• pp.45-50
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• 2005

In digital hearing aid system, one of the main problems is acoustic feedback which is known as howling because of miniaturization md high-gain amplification. In this paper, we proposed a feedback cancellation algorithm for hearing aid using time delay and time-varying decorrelation filter. The proposed algorithm has a kind of adaptive filter structure, which is combined with time delay and time-varying decorrelation filter to improve feedback cancellation. An all pass filter was implemented as the time-varying decorrelation filter using low frequency modulator. From the result of computer simulation, it is verified that the proposed algorithm has good ability to cancel feedback.