• Journal of Power System Engineering
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• v.18 no.1
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• pp.120-127
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• 2014

In this study, Design methods of stabilizing controller for time-delay pure singularly perturbed systems are proposed. Based on the Chang transformation and Lambert W function, we decompose the time-delayed pure singularly perturbed systems into completely decoupled subsystems and derive sufficient stability conditions for $2{\times}2$ time-delayed pure singularly perturbed systems. An illustrated example is presented to demonstrate the validity and applicability of the proposed methods.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.41 no.2
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• pp.29-36
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• 2004

This paper deals with a fractional model reduction for linear systems with time varying delayed states. A contractive coprime factorization of linear time delayed systems is defined and obtained by solving linear matrix inequalities. Using generalize controllability and observability gramians of tile contractive coprime factor, a balanced state space realization of the system is derived. The reduced model will be obtained by truncating states in the balanced realization and an upper bound of model approximation error is also presented. In order to demonstrate efficacy of the suggested method, a numerical example is illustrated.

• Journal of Mechanical Science and Technology
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• v.19 no.11
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• pp.1975-1987
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• 2005

An input time delay always exists in practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via digital computers. In this paper a new scheme for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption is proposed. The mathematical structure of the new discretization method is analyzed. On the basis of this structure the sampled-data representation of nonlinear systems with time-delayed multi-input is presented. The delayed multi-input general equation has been derived. In particular, the effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. Additionally, hybrid discretization schemes that result from a combination of the scaling and squaring technique (SST) with the Taylor series expansion are also proposed, especially under conditions of very low sampling rates. Practical issues associated with the selection of the method's parameters to meet CPU time and accuracy requirements, are examined as well. A performance of the proposed method is evaluated using a nonlinear system with time delay maneuvering an automobile.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.6
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• pp.120-127
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• 1995

A nonlinear empirical state-space model of the Artificial Neural Network(ANN) has been developed. The nonlinear model structure incorporates characteristic, so as to enable identification of the transient response, as well as the steady-state response of a dynamic system. A hybrid feedfoward/feedback neural network, namely a Local Time Delayed Recurrent Multi-layer Perception(RMLP), is the model structure developed in this paper. RMLP is used to identify nonlinear dynamic system in an input/output sense. The feedfoward protion of the network architecture provides with the well-known curve fitting factor, while local recurrent and cross-talk connections provides the dynamics of the system. A dynamic learning algorithm is used to train the proposed network in a supervised manner. The derived dynamic learning algorithm exhibit a computationally desirable characteristic; both network sweep involved in the algorithm are performed forward, enhancing its parallel implementation. RMLP state-space and its associate learning algorithm is demonstrated through a simple examples. The simulation results are very encouraging.

• Journal of Advanced Navigation Technology
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• v.21 no.6
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• pp.608-613
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• 2017

In this paper, we consider the stability bound for uncertainty of delayed state variables in the linear discrete interval time-varying systems with time-varying delay time. The considered system has an interval time-varying system matrix for non-delayed states and is perturbed by the unstructured time-varying uncertainty in delayed states with time-varying delay time within fixed interval. Compared to the previous results which are derived for time-invariant cases and can not be extended to time-varying cases, the new stability bound in this paper is applicable to time-varying systems in which every factors are considered as time-varying variables. The proposed result has no limitation in applicable systems and is very powerful in the aspects of feasibility compared to the previous. Furthermore. the new bound needs no complex numerical algorithms such as LMI(Linear Matrix Inequality) equation or upper solution bound of Lyapunov equation. By numerical examples, it is shown that the proposed bound is able to include the many existing results in the previous literatures and has better performances in the aspects of expandability and effectiveness.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1097-1107
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• 2009

In this paper, three species stage-structured predator-prey model with time delayed and periodic constant impulsive perturbations of predator at fixed times is proposed and investigated. We show that the conditions for the global attractivity of prey(pest)-extinction periodic solution and permanence of the system. Our model exhibits a new modelling method which is applied to investigate impulsive delay differential equations. Our results give some reasonable suggestions for pest management.

• Journal of Institute of Control, Robotics and Systems
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• v.15 no.4
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• pp.413-419
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• 2009

A decentralized adaptive control method is proposed for large-scale systems with unknown time-delayed nonlinear interconnections unmatched in control inputs. It is assumed that the time-delayed interaction terms are bounded by unknown nonlinear bounding functions. The nonlinear bounding functions and uncertain nonlinear functions of large-scale systems are compensated by the function approximation technique using neural networks. The dynamic surface control method is extended to design the proposed memoryless local controller for each subsystem of uncertain nonlinear large-scale time delay systems. Therefore, although the interconnected systems consist of a large number of subsystems, the proposed controller can be designed simply. We prove that all the signals in the total closed-loop system are semiglobally uniformly bounded and the control errors converge to an adjustable neighborhood of the origin. Finally, an example is given to demonstrate the effectiveness and applicability of the proposed scheme.

• Transactions on Control, Automation and Systems Engineering
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• v.2 no.4
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• pp.248-254
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• 2000

This paper presents and output feedback fuzzy H(sup)$\infty$ control problem for a class of nonlinear systems with time-varying delayed state. The Takagi-Sugeno fuzzy model is employed to represent a nonlinear systems with time-varying delayed state. Using a single quadratic Lyapunov function, the globally exponential stability and disturance attenuation of the closed-loop fuzzy control system are discussed. Sufficient conditions for the existence of fuzzy H(sup)$\infty$ controllers are given in terms of matrix inequalities. Constructive algorithm for design of fuzzy H(sup)$\infty$ controller is also developed. A simulation example is given to illustrate the performance of the proposed design method.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.331-331
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• 2000

This paper presents the mixed $H_2/H_{\infty}$ output feedback controIler design method for linear systems with delayed state. The objective is to design the output feedback controller which minimizes the H$_2$-norm of one transfer function while ensuring the H$_{\infty}$-norm of the other is held below a chosen level. When objective is tormulated in terms of a common Lyapunov function, the sufficient conditions of existence of mixed $H_2/H_{\infty}$ controller are given in terms of LMIs. terms of LMIs.

• Transactions on Control, Automation and Systems Engineering
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• v.2 no.4
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• pp.274-284
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• 2000

In this paper, the design methodology of digital fuzzy controller(DFC) for the systems with time-delay is presented and the qualitative effects of the quantizers in digital implementation of a fuzzy controllers are investigated. We propose the fuzzy feed-back controller whose output is delayed with unit sampling period and period and predicted. the analysis and the design problem considering time-delay become very easy because the proposed controller is syncronized with the sampling time. The stabilization problem of the digital fuzzy system with time-delay is solved by linear matrix inequality(LMI) theory. Furthermore, we analyze the stability of the quantized fuzzy system. Our results prove that when quantization os taken into account, one only has convergence to some small neighborhood about origin. We develop a fuzzy control system for backing up a computer-simulated truck-trailer with the consideration of time-delay and quantization effect. By using the proposed method, we analyze the quantization effect to the system and design a DFC which guarantees the stability of the control system in the presence of time-delay.