• International Journal of Control, Automation, and Systems
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• v.4 no.6
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• pp.682-688
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• 2006

This paper deals with the delay-dependent and rate-independent stabilization of systems with multiple unknown time-varying delays and time-varying structured uncertainties. All the linear matrix inequalities based conditions are derived by employing free-weighting matrices to express the relationships between the terms in the Leibniz-Newton formula. The criteria do not require any tuning parameters. Numerical examples demonstrate the validity of the method.

• 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.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.5
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• pp.580-585
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• 1999

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-bouded. 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.

• Journal of Institute of Control, Robotics and Systems
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• v.15 no.2
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• pp.121-127
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• 2009

This paper deals with the design problem of robust stabilization and non-fragile controller for discrete-time singular systems with parameter uncertainties and time-varying delays in state and input by delay-dependent Linear Matrix Inequality (LMI) approach. A new delay-dependent bounded real lemma for singular systems with time-varying delays is derived. Robust stabilization and robust non-fragile state feedback control laws are proposed, which guarantees that the resultant closed-loop system is regular, causal and stable in spite of time-varying delays, parameter uncertainties, and controller gain variations. A numerical example is given to show the validity of the design method.

• 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.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.113-116
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• 1997

In this paper, we present a robust $H^{\infty}$ controller design method for parameter uncertain time-varying systems with disturbance and that have time-varying delays in both state and control. It is found that the problem shares the same formulation with the $H^{\infty}$ control problem for systems without uncertainty. Through a certain differential Riccati inequality approach, a class of stabilizing continuous controller is proposed. For parameter uncertainties, disturbance and time varying delays, proposed controllers the plant and guarantee an $H^{\infty}$ norm bound constraint on disturbance attenuation for all admissible uncertainties. Finally a numerical example is given to demonstrate the validity of the results.ts.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.1
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• pp.181-186
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• 2009

In this paper, the stability analysis for uncertain dynamic systems with time-varying delays is considered. By constructing a new Lyapunov functional, a novel stability criterion is established in terms of linear matrix inequalities (LMIs). Two numerical examples are carried out to support the effectiveness of the proposed method.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.1051-1065
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• 2012

In this paper, the global stability and almost periodicity are investigated for generalized Hopfield neural networks with time-varying neutral delays. Some sufficient conditions are obtained for the existence and globally exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques. The results of this paper are new and complement previously known results. Finally, an example is given to demonstrate the effectiveness of our results.

• Journal of Electrical Engineering and Technology
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• v.6 no.5
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• pp.713-722
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• 2011

In the present paper, the problem of stability analysis for linear systems with interval time-varying delays is considered. By introducing a new Lyapunov-Krasovskii functional, new stability criteria are derived in terms of linear matrix inequalities (LMIs). Two numerical examples are given to show the superiority of the proposed method.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.63 no.7
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• pp.976-986
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• 2014

In this paper, the problem of reliable control of linear systems with time-varying delays, randomly occurring disturbances, and actuator failures is investigated. It is assumed that actuator failures occur when disturbances affect to the systems. Firstly, by using a suitable Lyapunov-Krasovskii functional and some recent techniques such as Wirtinger-based integral inequality and reciprocally convex approach, stabilization criterion for nominal systems with time-varying delays is derived. Secondly, the proposed method is extended to the reliable $H_{\infty}$ controller design for linear dynamic systems with time-varying delays, randomly occurring disturbances, and actuator failures. Since nonlinear matrix inequalities (NLMIs) are involved in proposed results, the cone complementarity algorithm will be introduced. Finally, two numerical examples are included to show the effectiveness of the proposed criteria.