• The Transactions of The Korean Institute of Electrical Engineers
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• v.64 no.7
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• pp.1096-1103
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• 2015

Electromagnetic levitation system(EMLS) is one of the well known nonlinear systems due to its high degree of nonlinearities. Moreover, when there are uncertain parameters in EMLS, it is not easy to have an accurate control of EMLS. In this paper, we first apply a standard input-output feedback linearzing controller to EMLS and investigate the possible control error caused by uncertain coil resistor. Then, as a remedy, we design and apply a robust controller using Lyapunov redesign technique to deal with this uncertain coil resistor in the system. The validity of our robust controller is verified via system analysis and experimental results.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.955-967
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• 2011

In this paper we have considered a nonautonomous predator-prey model with discrete time delay due to gestation, in which there are two prey habitats linked by isotropic migration. One prey habitat contains a predator and the other (a refuge) does not. Here, we have established some sufficient conditions on the permanence of the system by using in-equality analytical technique. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. We have observed that the per capita migration rate among two prey habitats and the time delay has no effect on the permanence of the system but it has an effect on the global asymptotic stability of this model. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-maker in targeting prevention and treatment resources for maximum effectiveness.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.279-292
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• 2011

In this paper, we consider anti-periodic solutions of the following BAM neural networks with multiple delays on time scales: $$\{{x^\Delta_i(t)=-a_i(t)e_i(x_i(t))+{\sum\limits^m_{j=1}}c_{ji}(t)f_j(y_j(t-{\tau}_{ji}))+I_i(t),\atop y^\Delta_j(t)=-b_j(t)h_j(y_j(t))+{\sum\limits^n_{i=1}}d_{ij}(t)g_i(x_i(t-{\delta}_{ij}))+J_j(t),}\$$ where i = 1, 2, ..., n,j = 1, 2, ..., m. Using some analysis skills and Lyapunov method, some sufficient conditions on the existence and exponential stability of the anti-periodic solution to the above system are established.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.387-397
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• 2017

In order to react the dynamic behavior of the system more actually, it is necessary to solve the first problem of synchronization for Markovian jump complex network system in practical engineering problem. In this paper, the problem of local stochastic synchronization for Markovian nonlinear coupled neural network system is investigated, including nonlinear coupling terms and mode-dependent delays, that is less restriction to other system. By designing the Lyapunov-Krasovskii functional and applying less conservative inequality, we get a new criterion to ensure local synchronization in mean square for Markovian nonlinear coupled neural network system. The criterion introduced some free matrix variables, which are less conservative. The simulation confirmed the validity of the conclusion.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.7
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• pp.901-908
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• 2003

Numerical study on stirring characteristics in a microchannel with blocks arranged periodically has been performed. Viscous flows through the microchannel is simulated three-dimensionally using a commercial code, FLUENT 6.0. Focus is given to the effect on the stirring characteristics of the geometric factors including the pitch, height and angle of the block arrangement. The numerical results at low Reynolds numbers show that the particles' trajectories in the microchannel heavily depend on the block arrangement. A nonlinear dynamical tool, i.e. Lyapunov exponent, was used in analysing the mixing effect. It was found that the mixing is the most effective at a certain combination of parameter values.

• Journal of Advanced Marine Engineering and Technology
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• v.20 no.2
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• pp.101-101
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• 1996

This paper presents the linearized fuzzy modeling technique of nonlinear dynamical system and the stability analysis of fuzzy control system. Firstly, the nonlinear system is partitionized by multiple linear fuzzy subcontrol systems based on fuzzy linguistic variables and fuzzy rules. Secondly, the disturbance adaptaion controllers which guarantee the global asymptotic stability of each fuzzy subsystem by an optimal feedback control law are designed and the stability analysis procedures of the total fuzzy control system using Lyapunov functions and eigenvalues are discussed in detail through a given illustrative example.

• Journal of Advanced Marine Engineering and Technology
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• v.20 no.2
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• pp.33-39
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• 1996

This paper presents the linearized fuzzy modeling technique of nonlinear dynamical system and the stability analysis of fuzzy control system. Firstly, the nonlinear system is partitionized by multiple linear fuzzy subcontrol systems based on fuzzy linguistic variables and fuzzy rules. Secondly, the disturbance adaptaion controllers which guarantee the global asymptotic stability of each fuzzy subsystem by an optimal feedback control law are designed and the stability analysis procedures of the total fuzzy control system using Lyapunov functions and eigenvalues are discussed in detail through a given illustrative example.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2004.10a
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• pp.193-200
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• 2004

In this paper, it is presented a new scheme of adaptive-neuro control system to implement real-time control of robot manipulator. Unlike the well-established theory for the adaptive control of linear systems, there exists relatively little general theory for the adaptive control of nonlinear systems. Adaptive control technique is essential for providing a stable and robust performance for application of robot control. The proposed neuro control algorithm is one of learning a model based error back-propagation scheme using Lyapunov stability analysis method. Through simulation, the proposed adaptive-neuro control scheme is proved to be a efficient control technique for real-time control of robot system using DSPs.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.8
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• pp.889-895
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• 2007

Quantifying dynamic stability is important to assessment of falling risk or functional recovery for leg injured people. Human locomotion is complex and known to exhibit nonlinear dynamical behaviors. The purpose of this study is to quantify major joints of the body using chaos analysis during walking. Time series of the chaotic signals show how gait patterns change over time. The gait experiments were carried out for ten young males walking on a motorized treadmill. Joint motions were captured using eight video cameras, and then three dimensional kinematics of the neck and the upper and lower extremities were computed by KWON 3D motion analysis software. The correlation dimension and the largest Lyapunov exponent were calculated from the time series to quantify stabilities of the joints. This study presents a data set of nonlinear dynamic characteristics for eleven joints engaged in normal level walking.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.89-102
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• 2010

This paper concerns the problem of global robust stability of a time-delay discontinuous system with a positive-defined connection matrix under polytopic-type uncertainty. In order to give the stability condition, we firstly address the existence of solution and equilibrium point based on the properties of M-matrix, Lyapunov-like approach and the theories of differential equations with discontinuous right-hand side as introduced by Filippov. Second, we give the delay-independent and delay-dependent stability condition in terms of linear matrix inequalities (LMIs), and based on Lyapunov function and the properties of the convex sets. One numerical example demonstrate the validity of the proposed criteria.