• Journal of Electrical Engineering and Technology
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• v.8 no.6
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• pp.1530-1541
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• 2013

The coexistence and extinction of species are important concepts for biological systems and can be distinguished by an investigation of stability. When determining local stability of nonlinear systems, Lyapunov indirect method based on the Jacobian linearization has been widely employed due to its simplicity. Despite such popularity, it is not applicable to singular systems whose Jacobian has at least one eigenvalue that is equal to zero. In such singular cases, an appropriate Lyapunov function should be sought to determine the stability of systems, which is rather difficult and quite involved. In this paper, we seek for a simple criterion to determine stability of the equilibrium that is located at the boundary of the positive orthant, when one of eigenvalues of the Jacobian is zero. The goal of the paper is to present a generalized condition for the equilibrium to attract all trajectories that starting from initial condition in the positive orthant and near the equilibrium. Unlike the Lyapunov direct method, the proposed method requires just a simple algebraic computation for checking the stability of the critical point. Our approach is applied to various biological systems to show the effectiveness of the proposed method.

• Advances in concrete construction
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• v.9 no.4
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• pp.407-412
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• 2020

Due to the influence of nonlinearity and time-variation, it is difficult to establish an accurate model of concrete frame structures that adopt active controllers. Fuzzy theory is a relatively appropriate method but susceptible to human subjective experience to decrease the performance. To guarantee the stability of multi-time delays complex system with multi-interconnections, a delay-dependent criterion of evolved design is proposed in this paper. Based on this criterion, the sector nonlinearity which converts the nonlinear model to multiple rule base of the linear model and a new sufficient condition to guarantee the asymptotic stability via Lyapunov function is implemented in terms of linear matrix inequalities (LMI). A numerical simulation for a three-layer reinforced concrete frame structure subjected to earthquakes is demonstrated that the proposed criterion is feasible for practical applications.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.9
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• pp.1748-1753
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• 2011

In this paper, we consider the stability of linear systems with an interval time-varying delay. It is known that the adoption of decomposition of delay improves the stability result. For the interval time-delay case, they applied it to the interval of time-delay and got less conservative results. Our basic idea is to apply the general decomposition to the low limit of delay as well as interval of time-delay. Based on this idea, by using the modified Lyapunov-Krasovskii functional and newly derived Lemma, we present a less conservative stability criterion expressed as in the form of linear matrix inequality(LMI). Finally, we show, by well-known two examples, that our result is less conservative than the recent results.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.55 no.4
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• pp.147-153
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• 2006

In this paper, we propose a new delay-dependent criterion on the robust stability of time-delayed linear systems having norm bounded uncertainties. Based on new form of Lyapunov-Krasovskii functional and the Newton-Leibniz formula, we drive a result in the form of LMI which guarantees the robust stability without any model transformation. The Newton-Leibniz equation was used to relate the cross terms with free matrices. Finally, we show the usefulness of our result by two numerical examples.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1072-1077
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• 2004

This paper provides a new approach to analyze the stability of a general multi-link TCP Vegas, which is a kind of feedback-based congestion algorithm. Whereas the conventional approaches use the approximately linearized model of the TCP Vegas along equilibrium pints, this approach models a multi-link TCP Vegas network in the form of a piecewise linear multiple time-delay system. And then, based on the exactly characterized dynamic model, this paper presents a new stability criterion via a piecewise and multiple delay-dependent Lyapunov-Krasovskii function. Especially, the resulting stability criterion is formulated in terms of linear matrix inequalities (LMIs).

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.961-972
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• 2008

In this paper, we consider the global exponential stability of cellular neural networks with time-varying delays. Based on the Lyapunov function method and convex optimization approach, a novel delay-dependent criterion of the system is derived in terms of LMI (linear matrix inequality). In order to solve effectively the LMI convex optimization problem, the interior point algorithm is utilized in this work. Two numerical examples are given to show the effectiveness of our results.

• Proceedings of the KIEE Conference
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• 2000.07d
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• pp.2320-2322
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• 2000

In this paper, the problem of the stability analysis for linear neutral delay-differential systems with nonlinear perturbations is investigated. Using Lyapunov second method, a new delay-dependent sufficient condition for asymptotic stability of the systems in terms of linear matrix inequalities (LMIs), which can be easily solved by various convex optimization algorithms, is presented. A numerical example is given to illustrate the proposed method.

• Computers and Concrete
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• v.30 no.5
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• pp.357-367
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• 2022

In this paper, we propose an efficient control method that can be transformed into a general building control problem for building structure control using these reliability criteria. To facilitate the calculation of controller H∞, an efficient solution method based on Linear Matrix Inequality (LMI) is introduced, namely H∞-based LMI control. In addition, a self-tuning predictive grey fuzzy controller is proposed to solve the problem caused by wrong parameter selection to eliminates the effect of dynamic coupling between degrees of freedom (DOF) in Self-Tuning Fuzzy Controllers. We prove stability using Lyapunov's stability theorem. To check the applicability of the proposed method, the proposed controller is applied and the control characteristics are determined. The simulation assumes system uncertainty in the controller design and emphasizes the use of acceleration feedback as a practical consideration. Simulation results show that the performance of the proposed controller is impressive, stable, and consistent with the performance of LMI-based methods. Therefore, an effective control method is suitable for seismic reinforcement of civil buildings.

• 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.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.2
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• pp.387-393
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• 2017

This paper focuses on a horizontal waypoint tracking and a speed control of large diameter unmanned underwater vehicles (LDUUVs) with X-stern configuration plane. The concerned design problem is converted into an asymptotic stabilization of the error dynamics with respect to the desired yaw angle and surge speed. It is proved that the error dynamics under the proposed control scheme based on the linear control and the feedback linearization can be considered as a cascade system; the cascade system is asymptotically stable if its nominal systems are so. This stability connection enables to separately deal with the waypoint tracking problem and the speed control one. By using the sector nonlinearity, the nominal system with nonlinearities is modeled as a polytopic linear parameter varying (LPV) system with parametric uncertainties. Then, sufficient linear matrix inequality (LMI) conditions for its asymptotic stabilizability are derived in the sense of Lyapunov stability criterion. An example is given to show the validity of the proposed methodology.