• 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.

• 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
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• v.62 no.4
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• pp.529-535
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• 2013

This paper considers the problem of robust stability for uncertain discrete-time interval time-varying delayed descriptor systems using any combinations of quantization and overflow nonlinearities. First, delay-dependent linear matrix inequality (LMI) condition for discrete-time descriptor systems with time-varying delay and quantization/overflow nonlinearities is presented by proper Lyapunov function. Second, it is shown that the obtained condition can be extended into descriptor systems with uncertainties such as norm-bounded parameter uncertainties and polytopic uncertainties by some useful lemmas. The proposed results can be applied to both descriptor systems and non-descriptor systems. Finally, numerical examples are shown to illustrate the effectiveness and less conservativeness.

• 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.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.10
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• pp.1854-1860
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• 2008

In this paper, we deal with the problem of delay-dependent robust and non-fragile stabilization for descriptor systems with parameter uncertainties and time-varying delays on the basis of strict LMI(linear matrix inequality) technique. Also, the considering controller is composed of multiplicative uncertainty. The delay-dependent robust and non-fragile stability criterion without semi-definite condition and decomposition of system matrices is obtained. Based on the criterion, the problem is solved via state feedback controller, which guarantees that the resultant closed-loop system is regular, impulse free and stable in spite of all admissible parameter uncertainties, time-varying delays, and controller fragility. Numerical examples are presented to demonstrate the effectiveness of the proposed method.

• 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.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.458-463
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• 1997

In this paper, we propose a variable structure control approach for the system with matched and unmatched uncertainty. By using time-varying sliding mode, the reaching mode is removed, and the design methodology represents a realistic design approach with quadratic criterion for systems incorporating both matched and unmatched uncertainties. The criterion contains states and linear part of input for all time. The practical application of the control strategy is presented in the design of a stability augmentation system for an aircraft is presented.

• Journal of Electrical Engineering and Technology
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• v.11 no.1
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• pp.200-214
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• 2016

This paper investigates the problem of stability analysis and robust H_∞ controller for time-delayed systems with parameter uncertainties and stochastic disturbances. It is assumed parameter uncertainties are norm bounded and mean and variance for disturbances of them are known. Firstly, by constructing a newly augmented Lyapunov-Krasovskii functional, a stability criterion for nominal systems with time-varying delays is derived in terms of linear matrix inequalities (LMIs). Secondly, based on the result of stability analysis, a new controller design method is proposed for the nominal form of the systems. Finally, the proposed method is extended to the problem of robust H_∞ controller design for a time-delayed system with parameter uncertainties and stochastic disturbances. To show the validity and effectiveness of the presented criteria, three examples are included.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.1
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• pp.13-18
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• 2005

This paper considers a design problem of the repetitive control system for linear systems with time-varying norm bounded uncertainties. Using the Lyapunov functional for time-delay systems, a sufficient condition ensuring robust stability of the repetitive control system is derived in terms of an algebraic Riccati inequality (ARI) or a linear matrix inequality (LMI). Based on the derived condition, we show that the repetitive controller design problem can be reformulated as an optimization problem with an LMI constraint on the free parameter.

• 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.