• Journal of Institute of Control, Robotics and Systems
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• v.5 no.6
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• pp.641-646
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• 1999

This paper deals with the robust stability of discrete-time linear systems with time- varying delays and norm-bounded uncertainties. In this paper, the magnitude of time-varying delays is assumed to be upper-bounded. The sufficient condition is presented in terms of linear matrix inequality. It is also shown that the robust stability of uncertain discrete-time linear systems with time-varying delays is related with the quadratic stability of uncertain discrete-time linear systems with constant time delay.

• 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 applied mathematics & informatics
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• v.9 no.1
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• pp.61-76
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• 2002

The robust non-fragile guaranteed cost control problem is studied in this paper for class of uncertain linear large-scale systems with time-varying delays in subsystem interconnections and given quadratic cost functions. The uncertainty in the system is assumed to be norm-hounded arid time-varying. Also, the state-feedback gains for subsystems of the large-scale system are assumed to have norm-bounded controller gain variations. The problem is to design state feedback control laws such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound far all admissible uncertainties. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. A parameterized characterization of the robust non-fragile guaranteed cost contrellers is 7iven in terms of the feasible solution to a certain LMI. Finally, in order to show the application of the proposed method, a numerical example is included.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.11
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• pp.2261-2265
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• 2009

In this paper, the problem of delay-dependent stability of uncertain stochastic systems with time-varying delay is considered. The uncertainties are assumed to be norm-bounded. Based on the Lyapunov stability theory, new delay-dependent stability criteria for the system are derived in terms of LMI(linear matrix inequality). Two numerical examples are given to show the effectiveness of proposed method.

• 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.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.39 no.6
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• pp.20-26
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• 2002

This paper deals with the guaranteed cost control problems for a class of discrete-time linear uncertain systems with time-varying delay. The uncertain systems under consideration depend on time-varying norm-bounded parameter uncertainties. We address the existence condition and the design method of the memoryless state feedback control law such that the closed loop system not only is quadratically stable but also guarantees an adequate level of performance for all admissible uncertainties. Through some changes of variables and Schur complement, It is shown that the sufficient condition can be rewritten as an LMI(linear matrix inequality) form in terms of all variables.

• Proceedings of the KIEE Conference
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• 2004.11c
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• pp.379-381
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• 2004

In this paper, a robust $H_{\infty}$ stabilization problem to a uncertain 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.

• Journal of Electrical Engineering and Technology
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• v.8 no.6
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• pp.1542-1550
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• 2013

This paper presents new results on delay-dependent global exponential stability for uncertain linear systems with interval time-varying delay. Based on Lyapunov-Krasovskii functional approach, some novel delay-dependent stability criteria are derived in terms of linear matrix inequalities (LMIs) involving the minimum and maximum delay bounds. By using delay-partitioning method and the lower bound lemma, less conservative results are obtained with fewer decision variables than the existing ones. Numerical examples are given to illustrate the usefulness and effectiveness of the proposed method.

• 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.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.199-199
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• 2000

Most of linear time-varying(LTV) systems except special cases have no general solution for the dynamic equations. Thus, it is difficult to design time-varying controllers in analytic ways, and other control design approaches such as robust control have been applied to control design for uncertain LTI systems which are the approximation of LTV systems have been generally used instead. A robust control method such as quantitative feedback theory(QFT) has an advantage of guaranteeing the stability and the performance specification against plant parameter uncertainties in frozen time sense. However, if these methods are applied to the approximated linear time-invariant(LTI) plants which have large uncertainty, the designed control will be constructed in complicated forms and usually not suitable for fast dynamic performance. In this paper, as a method to enhance the fast dynamic performance, the approximated uncertainty of time-varying parameters are reduced by the proposed QFT parameter-scheduling control design based on radial basis function (RBF) networks for LTV systems with bounded time-varying parameters.