• 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 Mechanical Science and Technology
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• v.17 no.4
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• pp.484-491
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• 2003

For most of linear time-varying (LTV) systems, it is difficult to design time-varying controllers in analytic way. Accordingly, by approximating LTV systems as uncertain linear time-invariant, control design approaches such as robust control have been applied to the resulting uncertain LTI systems. In particular, a robust control method such as quantitative feedback theory (QFT) has an advantage of guaranteeing the frozen-time stability and the performance specification against plant parameter uncertainties. However, if these methods are applied to the approximated linear. time-invariant (LTI) plants with large uncertainty, the resulting control law becomes complicated and also may not become ineffective with faster dynamic behavior. In this paper, as a method to enhance the fast dynamic performance of LTV systems with bounded time-varying parameters, the approximated uncertainty of time-varying parameters are reduced by the proposed QFT parameter-scheduling control design based on radial basis function (RBF) networks.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.54 no.6
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• pp.315-322
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• 2005

In this article, 1 would like to explore the estimation method of time-varying voltage sags in large industrial systems considering the short circuit contributions of rotating machines. For the power distribution system of KEPCO(Korea Electric Power Corporation), the magnitude of initial symmetrical short circuit current is generally not changed. However, in industrial systems which contain a number of rotating machines, the magnitude of voltage sag is generally changed from the initial to the clearing time of a fault due to the decreasing contribution of rotating machines for a fault current. The time-varying characteristics of voltage sags can be calculated using a short circuit analysis that is considered the time-varying fault currents. For this, the prediction formulations of time-varying voltage sags are proposed using a foreign standard. The proposed method contains the consideration of generator and motor effects. For the test of proposed formulations, a simple system of industrial consumer is used for the comparison conventional and proposed estimation method of voltage sag characteristics.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.125.1-125
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• 2001

This paper deals with the eigenvalue assignment technique for linear time-varying systems to achieve feedback stabilization. For this, we introduce the novel eigenvalue concepts. Then, we propose the Ackerman-like formula for linear time-varying systems. It is believed that this technique is the generalized version of the Ackerman formula forlinear time-invariant systems. The advantages of the proposed technique are that it does not require the transformation of the original system into the phase-variable form nor the computation of eigenvalues of the original system.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.6
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• pp.647-655
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• 1999

For linear time-varying systems described by the triple (A(t),B(t),C(t)) where A(t),B(t),C(t) are the system, the input, and the output matrices, respectively, we propose concepts for measures of modal and gross controllability /observability. We introduce a differential algebraic eigenbvalue theory for linear time-varying systems to calculate the PD-eigenvalues and left and right PD-eigenvectors of the system matrix A(t) which will be used to derive the concepts for the measures. The time-dependent angle between the left PD-eigenvectors of the system matrix A(t) and the columns of the input matrix B(t), and the magnitude of the each element of the input matrix B(t) are used to propose the modal controllability measure. Similarly, the time-dependent angle between the right PD-eigenvectors of the system matrix A(t) and the rows of the output matrix C(t) are used to propose the madal observability measure. Gross measure of controllability of a mode from all inputs and its gross measure of observability in all outputs for the linear time-varying systems are also proposed. Numerical examples are presented to illustrate the proposed concepts.

• Journal of Institute of Control, Robotics and Systems
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• v.16 no.2
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• pp.140-144
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• 2010

In the case of a linear time-varying system, it is difficult to apply the conventional stability conditions of RHC (Receding Horizon Control) to real physical systems because of computational complexity comes from time-varying system and backward Riccati equation. Therefore, in this study, a frozen time RHC for a linear discrete time-varying system is proposed. Since the proposed control law is obtained by time-invariant Riccati equation solved by forward iterations at each control time, its stability can be ensured by matrix inequality condition and the stability condition based on horizon for a time-invariant system, and they can be applied to real physical systems effectively in comparison with the conventional RHC.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.5
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• pp.521-528
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• 1999

The nth-order, scalar, linear time-varying (LTV) systems can be dealt with operators on a differential ring. Using this differential algebraic structure and a classical result on differential operator factorizaitons developed by Floquet, a novel eigenstructure(eigenvalues, eigenvectors) concepts for linear time0varying systems are proposed. In this paper, Necessary and sufficient conditions for the existence of well-defined(free of finite-time singularities) SD- and PD- spectra for SPDOs with complex- and real-valued coefficients are also presented. Three numerical examples are presented to illustrate the proposed concepts.

• Proceedings of the KIEE Conference
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• 1998.07b
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• pp.641-643
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• 1998

This paper deals with the stability of discrete time linear systems with time - varying delays in state. In this paper, the magnitude of time - varying delays is assumed to be upper-bounded. The stability of discrete time linear systems with time - varying delays in state is related with the stability of discrete time linear systems with constant time delay in state. To show this, a new Lyapunov function is proposed. Using this Lyapunov function, a sufficient condition for the asymptotic stability is derived.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.04a
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• pp.149-152
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• 2005

In this paper, a robust $H\infty$ stabilization problem to a uncertain discrete-time fuzzy systems with time-varying delay via static output feedback is investigated. The Takagi -Sugeno (T-S) fuzzy model is employed to represent an uncertain nonlinear systems with time-varying delayed state. Using a single Lyapunov function, the globally asymptotic stability and disturbance attenuation of the closed-loop fuzzy control system are discussed. Sufficient conditions for the existence of robust $H\infty$ controllers are given in terms of linear matrix inequalities.

• KIEE International Transaction on Systems and Control
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• v.12D no.1
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• pp.39-42
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• 2002

This paper focuses on the asymptotic stability of a class of neutral linear systems with mixed time-varying delay arguments. Using the Lyapunov method, a delay-dependent stability criterion to guarantee the asymptotic stability for the systems is derived in terms of linear matrix inequalities (LMIs). The LMIs can be easily solved by various convex optimization algorithms. Two numerical examples are given to illustrate the proposed methods.