• 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.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.64 no.1
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• pp.121-127
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• 2015

This paper considers the problem of sampled-data control for continuous linear parameter varying (LPV) systems. It is assumed that the sampling periods are arbitrarily varying but bounded. Based on the input delay approach, the sampled-data control LPV system is transformed into a continuous time-delay LPV system. Some less conservative stabilization results represented by LMI (Linear Matrix Inequality) are obtained by using the Lyapunov-Krasovskii functional method and the reciprocally combination approach. The proposed method for the designed gain matrix should guarantee asymptotic stability and a specified level of performance on the closed-loop hybrid system. Numerical examples are presented to demonstrate the effectiveness and the improvement of the proposed method.

• Transactions on Control, Automation and Systems Engineering
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• v.2 no.1
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• pp.19-23
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• 2000

In this paper, we deal with the problem of designing guaranteed cost state feedback controller for the generalized time-varying delay systems with delayed state and control input. The generalized time delay system problems solved on the basis of LMI(linear matrix inequality) technique considering time-varying delays. The sufficient condition for the existence of controller and guaranteed cost state feedback controller design methods are presented. Also, using some changes of variables and Schur complements, the obtained sufficient condition can be reformulated as LMI forms in terms of transformed variables. Therefore, all solutions of LMIs, guaranteed cost controller gain, and guaranteed cost are obtained at the same time. The proposed controller design method can be extended into the problem of robust guaranteed cost controller design method for parameter uncertain systems with time-varying delays easily.

• Journal of Advanced Navigation Technology
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• v.17 no.6
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• pp.679-686
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• 2013

In this paper, the new stability conditions for discrete systems with time-varying delay time are proposed by Lyapuniv theory for the stability analysis of NCS(Networked Control System) having data communication. The proposed stability conditions are very simple and easily calculated compared to the previous conditions having complex numerical calculations. The proposed results can include several previous works on the same issue. From the simulation results, the proposed conditions show the better performance and less conservative on checking stability compared with previous results.

• 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.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.7
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• pp.1019-1023
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• 2012

This paper considers a model predictive control problem of discrete-time constrained systems with time-varying delay. For this problem, a delay dependent state feedback control approach is used to achieve asymptotic stabilization of systems with input constraints. Based on Lyapunov stability theory, a new stability condition is obtained via linear matrix inequality formulation to find cost monotonicity condition of the model predictive control algorithm which guarantee the closed loop stability. Finally, the proposed method is applied to a numerical example in order to show the effectiveness of our results.

• Journal of Advanced Navigation Technology
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• v.22 no.6
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• pp.630-635
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• 2018

In this paper, we consider the stability condition for the linear discrete systems with time-varying delay and unstructured uncertainty. The considered system has time invariant system matrices for non-delayed and delayed state variables, but its delay time is time-varying within certain interval and it is subjected to nonlinear unstructured uncertainty which only gives information on uncertainty magnitude. In the many previous literatures, the time-varying delay and unstructured uncertainty can not be dealt in simultaneously but separately. In the paper, new stability conditions are derived for the case to which two factors are subjected together and compared with the existing results considering only one factor. The new stability conditions improving many previous results are proposed as very effective inequality equations without complex numerical algorithms such as LMI(Linear Matrix Inequality) or Lyapunov equation. By numerical examples, it is shown that the proposed conditions are able to include the many existing results and have better performances in the aspects of expandability and effectiveness.

• 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.

• Nonlinear Functional Analysis and Applications
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• v.29 no.3
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• pp.803-823
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• 2024

In this paper, we study the existence and uniqueness of solutions for the fractional time-varying delay integrodifferential equation with multi-point multi-term nonlocal and fractional integral boundary conditions by using fixed point theorems. The fractional derivative considered here is in the Caputo sense. Examples are provided to illustrate the results.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.6
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• pp.554-557
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• 2008

We analyze the stability property of a class of nonlinear time-delay systems with time-varying delays. We present a time-delay independent sufficient condition for the global asymptotic stability. In order to prove the sufficient condition, we exploit the inherent property of the considered systems instead of applying the Krasovskii or Razumikhin stability theory that may cause the mathematical difficulty of analysis. We prove the sufficient condition by constructing two sequences that represent the lower and upper bound variations of system state in time, and showing the two sequences converge to an identical point, which is the equilibrium point of the system. The simulation results illustrate the validity of the sufficient condition for the global asymptotic stability.