• 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 Advanced Navigation Technology
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• v.24 no.6
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• pp.549-556
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• 2020

This paper proposes several suboptimal methods of designing a controller for a networked control system with state feedback where delay due to transmission error and transmission delay is modeled as a Markov process. A stability condition for a control system with Markov delay is found through an equivalent relationship that corresponding delay-dependent Lyapunov-Krasovskii functional has the same form of the Lyapunov function of an augmented control system. Several suboptimal methods of designing a controller from the stability condition are proposed to reduce complexity. A simple numerical experiment shows that a restricted subspace method which limits the search space of a matrix variable to a block diagonal form provides the best tradeoff between the complexity and performance.

• Journal of Institute of Control, Robotics and Systems
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• v.19 no.3
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• pp.183-189
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• 2013

This paper presents a stabilization method for NCS (Networked Control Systems) with two additive time-varying delays. Each time delay component between the plant and the controller has different characteristics depending on communication network, and has the upper and lower bounds. The time delay occurring from the controller to the plant has an effect on the time delay occurring from the plant to the controller, and the relationship between two delays is taken into account on the stability analysis. Based on the two additive delay components and the bound conditions, the appropriate Lyapunov-Krasovskii functional and the LMI (Linear Matrix Inequality) method derive the stability condition and the $H_{\infty}$ norm constraint for time-varying delayed NCS. Simulation results are finally given to demonstrate the effectiveness of the proposed method.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.63 no.4
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• pp.502-508
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• 2014

In this paper, a delay-dependent $H_{\infty}$ filtering problem is investigated for discrete-time delayed nonlinear systems which include a more general sector nonlinear function instead of employing the commonly used Lipschitz-type function. By using the Lyapunov-Krasovskii functional approach, a less conservative sufficient condition is established for the existence of the desired filter, and then, the corresponding solvability condition guarantee the stability of the filter with a prescribed $H_{\infty}$ performance level. Finally, two simulation examples are given to show the effectiveness of the proposed filtering scheme.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.5
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• pp.806-811
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• 2017

This paper considers the delay-dependent stability of linear systems with a time-varying delay in the frame work of Lyapunov-Krasovskii functional(LKF) approach. In this approach, an integral inequality is essential to estimate the upper bound of time-derivative of LKF, and a less conservative one is needed to get a less conservative stability result. In this paper, based on free weighting matrices, an improved integral inequality encompassing well-known results is proposed and then a stability result in the form of linear matrix inequality is derived based on an augmented LKF. Finally, two well-known numerical examples are given to demonstrate the usefulness of the proposed result.

• Journal of IKEEE
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• v.20 no.4
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• pp.378-384
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• 2016

This paper addresses the output feedback consensus problem for high-order integrators under a directed network with a communication delay. In order to solve this problem, the dynamic output feedback controller is proposed. Also, by using Lyapunov-Krasovskii functional, it is shown that the existence of the proposed consensus controller can always be guaranteed even in the presence of an arbitrarily large communication delay.

• 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.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.3
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• pp.187-191
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• 2007

We analyze the stability property of a class of nonlinear time-delay systems. We show that the state variable is bounded both below and above, and the lower and upper bounds of the state are obtained in terms of a system parameter by using the comparison lemma. We establish a time-delay independent sufficient condition for the global asymptotic stability by employing a Lyapunov-Krasovskii functional obtained from a change of the state variable. The simulation results illustrate the validity of the sufficient condition for the global asymptotic stability.

• International Journal of Control, Automation, and Systems
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• v.6 no.4
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• pp.515-525
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• 2008

In this paper, the problem of delay-dependent stabilization for singular systems with multiple internal and external incommensurate constant point delays is investigated. The condition when a singular system subject to point delays is regular independent of time delays is given and it can be easily test with numerical or algebraic methods. Based on Lyapunov-Krasovskii functional approach and the descriptor integral-inequality lemma, a sufficient condition for delay-dependent stability is obtained. The main idea is to design multiple memoryless state feedback control laws such that the resulting closed-loop system is regular independent of time delays, impulse free, and asymptotically stable via solving a strict linear matrix inequality (LMI) problem. An explicit expression for the desired memoryless state feedback control laws is also given. Finally, a numerical example illustrates the effectiveness and the availability for the proposed method.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.3
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• pp.337-342
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• 2009

This paper concerns delay-range-dependent robust stability and stabilization for time-delay nonliner system via T-S fuzzy model approach. The time delay is assumed to be a time-varying continuous function belonging to a given range. On the basis of a novel Lyapunov-Krasovskii functional, which includes the information of the range, delay-range-dependent stability criteria are established in terms of linear matrix inequality. It is shown that the new criteria can provide less conservative results than some existing ones. Moreover, the stability criteria are also used to design the stabilizing state-feedback controllers. Numerical examples are given to demonstrate the applicability of the proposed approach.