• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1193-1198
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• 2012

By constructing suitable Lyapunov functionals and combining with matrix inequality technique, a new simple sufficient condition is presented for the global asymptotic stability of the Cohen-Grossberg neural network models. The condition contains and improves some of the previous results in the earlier references.

• IEMEK Journal of Embedded Systems and Applications
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• v.16 no.4
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• pp.119-127
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• 2021

The aim of this paper is to propose a less conservative stabilization condition for leader-following sampled-data control of wheeled mobile robot (WMR) systems by using a clock-dependent Lyapunov function (CDLF) with looped functionals. In the leader-following WMR system, the state and input of the leader robot are measured by digital devices mounted on the following robot, and they are utilized to construct the sampled-data controller of the following robot. To design the sampled-data controller, a stabilization condition is derived by using the CDLF with looped functionals, and formulated in terms of sum of squares (SOS). The considered Lyapunov function is a polynomial form with respect to the clock related to the transmitted sampling instants. As the degree of the Lyapunov function increases, the stabilization condition becomes less conservative. This ensures that the designed controller is able to stabilize the system with a larger maximum sampling interval. The simulation results are provided to demonstrate the effectiveness of the proposed method.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1921-1930
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• 2018

We consider a functional difference equation and use fixed point theory to obtain necessary and sufficient conditions for the asymptotic stability of its zero solution. At the end of the paper we apply our results to nonlinear Volterra infinite delay difference equations.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.195-204
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• 2014

We consider a functional difference equation and use fixed point theory to analyze the stability of its zero solution. In particular, our study focuses on the nonlinear delay functional difference equation x(t + 1) = a(t)g(x(t - r)).

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.9
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• pp.4342-4366
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• 2016

Congestion control in Cluster Wireless Sensor Networks (CWSNs) has drawn widespread attention and research interests. The increasing number of nodes and scale of networks cause more complex congestion control and management. Active Queue Management (AQM) is one of the major congestion control approaches in CWSNs, and Random Early Detection (RED) algorithm is commonly used to achieve high utilization in AQM. However, traditional RED algorithm depends exclusively on source-side control, which is insufficient to maintain efficiency and state stability. Specifically, when congestion occurs, deficiency of feedback will hinder the instability of the system. In this paper, we adopt the Additive-Increase Multiplicative-Decrease (AIMD) adjustment scheme and propose an improved RED algorithm by using neighbor feedback and scheduling scheme. The congestion control model is presented, which is a linear system with a non-linear feedback, and modeled by Lur'e type system. In the context of delayed Lur'e dynamical network, we adopt the concept of cluster synchronization and show that the congestion controlled system is able to achieve cluster synchronization. Sufficient conditions are derived by applying Lyapunov-Krasovskii functionals. Numerical examples are investigated to validate the effectiveness of the congestion control algorithm and the stability of the network.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.10
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• pp.1894-1899
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• 2010

This note is concerned with a robust sliding mode control(SMC) for a class of unmatched uncertain system with severe commensurate state time delay. The suggested method is extended to the control of severe state time delay systems with unmatched uncertainties except the matched input matrix uncertainty. A transformed sliding surface is proposed and a stabilizing control input is suggested. The closed loop stability together with the existence condition of the sliding mode on the proposed sliding surface is investigated through one Lemma and two Theorems by using the Lyapunov direct method with the concept of the control Lyapunov function instead of complex Lyapunov-Kravoskii functionals. Through an illustrative example and simulation study, the usefulness of the main results is verified.

• Journal of Institute of Control, Robotics and Systems
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• v.20 no.3
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• pp.289-297
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• 2014

This article surveys the control theoretic study on time delay systems. Since time delay systems are infinite dimensional, there are not analytic but numerical solutions on almost analysis and synthesis problems, which implies that there are a tremendous number of approximated solutions. To show how to find such solutions, several results are summarized in terms of two different axes: 1) theoretic tools like integral inequality associated with the derivative of delay terms, Jensen inequality, lower bound lemma for reciprocal convexity, and Wirtinger-based inequality and 2) various candidates for Laypunov-Krasovskii functionals.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.907-914
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• 2015

In this paper, we consider a viscoelastic plate equation with p-Laplacian $u^{{\prime}{\prime}}+{\Delta}^2u-div({\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)+{\sigma}(t){\int}_{0}^{t}g(t-s){\Delta}u(s)ds-{\Delta}u^{\prime}=0$. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of both ${\sigma}$ and g.

• Proceedings of the KIEE Conference
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• 2007.07a
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• pp.1674-1675
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• 2007

This paper presents a stability analysis of network systems with time delay. Time delay problem frequently occurs in network systems. Since it makes network systems unstable and unpredictable, an optimal controller is necessary to network systems. We prove the asymptotical stability of time delayed network systems using LMI optimization method and appropriate Lyapunov-Krasovskii functionals. Simulations show the effectiveness of the method.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.8
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• pp.1464-1470
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• 2010

In this paper, we consider the $H_{\infty}$ control of time-delayed linear systems with saturating actuators. The considered time-delay is a time-varying one having bounds on magnitude and time-derivative, and the control permits the predetermined degree of saturation. Based on two modified Lyapunov-Krasovskii(L-K) functionals, we derive a $H_{\infty}$ control in the form of linear matrix inequalities(LMI) having three non-convex design parameters. The result is dependent on the characteristics of time-delay, predetermined degree of saturation level, and bound of disturbance. Finally, we give a comparative example to show the effectiveness and usefulness of our result.