• Journal of Institute of Control, Robotics and Systems
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• v.4 no.1
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• pp.1-9
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• 1998

This paper is focussed on the problem of robustly stabilizing a transformable linear time-varying system. The considered system is a class of state feedback transformable linear systems. First, the real linear time-varying system is transformed into the linear time invariant system composed with the time-invariant linear part and the time-varying uncertainty part. Second, the solution to a quadratic stabilization problem in the transformed linear system is give via' Lyapunov methods. Then this solution is used to construct a stabilizing linear control law for the real linear time-varying system.

• Journal of Institute of Convergence Technology
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• v.5 no.2
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• pp.37-42
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• 2015

This paper presents the effects of the computational time-varying delay on the stability of the haptic system that includes a virtual wall and a first-order-hold method. The model of a haptic system includes a haptic device model with a mass and a damper, a virtual wall model, a first-order-hold model and a computational time-varying delay model. In this paper, the maximum of the computational time-varying delay is assumed to be as much as the sampling time. Using the simulation, it is analyzed how the sample-hold methods and the computational time-varying delay affect the maximum available stiffness. As the maximum of computational time-varying delay increases, the maximal available stiffness of a virtual wall model is reduced.

• 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 Advanced Navigation Technology
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• v.20 no.5
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• pp.475-481
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• 2016

In this paper, the new stability condition of linear discrete interval time-varying systems with time-varying delay time is proposed. The considered system has interval time-varying system matrices for both non-delayed and delayed states with time-varying delay time within given interval values. The proposed condition is derived by using Lyapunov stability theory and expressed by very simple inequality. The restricted stability issue on the interval time-invariant system is expanded to interval time-varying system and a powerful stability condition which is more comprehensive than the previous is proposed. As a results, it is possible to avoid the introduction of complex linear matrix inequality (LMI) or upper solution bound of Lyapunov equation in the derivation of sufficient condition. Also, it is shown that the proposed result can include the many existing stability conditions in the previous literatures. A numerical example in the pe revious works is modified to more general interval system and shows the expandability and effectiveness of the new stability condition.

• Journal of Institute of Control, Robotics and Systems
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• v.22 no.6
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• pp.424-428
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• 2016

A simple new sufficient condition for asymptotic stability of the positive linear time-varying discrete-time systems, with unstructured time-varying uncertainty in delayed states, is established in this paper Compared with previous results that cannot be applied to time-varying systems; the time-varying system and delay time are considered simultaneously in this paper. The proposed conditions are compared with suitable conditions for the typical discrete-time systems. The considerations are illustrated by numerical examples of previous work.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.53 no.12
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• pp.793-798
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• 2004

In this paper, the problem of adaptively identifying time-varying nonlinear systems is considered. For that purpose, the discrete time-varying Volterra series is employed as a system model, and the filtered weighted least squares (FWLS) algorithm, developed for adaptive identification of linear time-varying systems, is utilized for the adaptive identification of time-varying quadratic Volterra systems. To demonstrate the performance of the proposed approach, some simulation results are provided. Note that the FWLS algorithm, decomposing the conventional weighted basis function (WBF) algorithm into a cascade of two (i.e., estimation and filtering) procedures, leads to fast parameter tracking with low computational burden, and the proposed approach can be easily extended to the adaptive identification of time-varying higher-order Volterra systems.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.62.2-62
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• 2001

In this paper, we present a new time-varying sliding mode system that guarantees stable error convergence. The previous papers have dealt with stability of the time-varying sliding mode system by point-wisely investigating the stability of time-invariant system every time. However, it may be unstable even though it guarantees time-invariant stability every time, We designed the time-varying sliding surface so that the resultant time-varying system on sliding mode may be Stable. The initial sliding surface is obtained so that shifting distance of the surface may be minimized with respect to an initial error, and the intercept is produced so that the surface may pass the initial error.

• 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 Advanced Navigation Technology
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• v.18 no.5
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• pp.501-507
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• 2014

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, new sufficient conditions for asymptotic stability of the interval positive time-varying linear discrete-time systems with time-varying delay in states are considered. The considered time-varying delay time has an interval-like bound which has minimum and maximum delay time. The proposed conditions are established by using a solution bound of the Lyapunov equation and they are expressed by simple inequalities which do not require any complex numerical algorithms. An example is given to illustrate that the new conditions are simple and effective in checking stability for interval positive time-varying discrete systems.

• Journal of Advanced Navigation Technology
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• v.27 no.6
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• pp.871-876
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• 2023

In this paper, we deal with the stable conditions when two uncertainties exist simultaneously in a linear discrete time-varying interval system with time-varying delay time. The interval system is a system in which system matrices are given in the form of an interval matrix, and this paper targets the system in which the delay time of these interval system matrices and state variables is time-varying. We propose the system stability condition when there is simultaneous unstructured uncertainty that includes nonlinearity and only its magnitude and uncertainty in the system matrix of delayed state variables. The stable bounds for two types of uncertainty are derived as an analytical equation. The proposed stability condition and bounds can include previous stability condition for various linear discrete systems, and the values such as time-varying delay time variation size, uncertainty size, and range of interval matrix are all included in the conditional equation. The new bounds of stability are compared with previous results through numerical example, and its effectiveness and excellence are verified.