• International Journal of Control, Automation, and Systems
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• 제4권5호
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• pp.545-558
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• 2006

In this paper, PD-like visual servoing is modified in two ways: a sliding-mode observer is applied to estimate the joint velocities, and a RBF neural network is used to compensate the unknown gravity and friction. Based on Lyapunov method and input--to-state stability theory, we prove that PD-like visual servoing with the sliding mode observer and the neuro compensator is robust stable when the gain of the PD controller is bigger than the upper bounds of the uncertainties. Several simulations are presented to support the theory results.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2000년도 하계학술대회 논문집 D
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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.

• 한국정밀공학회지
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• 제22권4호
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• pp.128-135
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• 2005

Overhead crane systems consist of trolley, girder, rope, objects, trolley motor, girder motor, and hoist motor. The dynamic system of these systems becomes a nonlinear state equations. These equations are obtained by the nonlinear equations of motion which are derived from transfer functions of driving motors and equations of motion for objects. From these state equations, Lyapunov functions of overhead crane systems are derived from integral method. These functions secure stability of autonomous overhead crane systems. Also constraint equations of driving motors of trolley, girder, and hoist are derived from these functions. From the results of computer simulation, it is founded that overhead crane systems is secure.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1117-1127
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• 2011

In this paper, a class of more general delayed viral infection model with lytic immune response is proposed by Song et al.[1] ([Journal of Mathematical Analysis Application 373 (2011), 345-355). We derive the basic reproduction numbers $R_0$ and $R_0^*$ 0 for the viral infection, and establish that the global dynamics are completely determined by the values of $R_0$ and $R_0^*$. If $R_0{\leq}1$, the viral-free equilibrium $E_0$ is globally asymptotically stable; if $R_0^*{\leq}1$ < $R_0$, the immune-free equilibrium $E_1$ is globally asymptotically stable; if $R_0^*$ > 1, the chronic-infection equilibrium $E_2$ is globally asymptotically stable by using the method of Lyapunov function.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2003년도 학술회의 논문집 정보 및 제어부문 A
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• pp.247-250
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• 2003

In this paper, we propose a robust controller for motion control of n-link robot manipulators using visual feedback. The desired joint velocity and acceleration is obtained by the feature-based visual systems and is used in the joint velocity control loop for trajectory control of the robot manipulator. We design a robust controller that compensates for bounded parametric uncertainties of robot dynamics. The stability analysis of robust joint velocity control system is shown by Lyapunov Method. The effectiveness of the proposed method is shown by simulation results on the 5-link robot manipulators with two degree of freedom.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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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.

• 전기학회논문지
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• 제58권2호
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• pp.314-321
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• 2009

In this paper, the robust nonlinear observer will be developed for PEM fuel cell system. Nonlinear model of PEM fuel cell system is introduced to study the design problems of observer. Sliding mode observer is designed to estimate the cathode and anode pressures of PEMFC system. And a nonlinear state observer is also designed to estimate the other states such as supply manifold pressure, Oxygen pressure, Hydrogen pressure, return manifold pressure, etc. The validity of the proposed observer will be verified by using Lyapunov's stability analysis method.

• Advances in nano research
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• 제15권1호
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• pp.25-34
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• 2023

This paper investigates the dynamics and stability of steady states in a continuous and discrete-time single-mode laser system. By using an explicit criteria we explored the Neimark-Sacker bifurcation of the single mode continuous and discrete-time laser model at its positive equilibrium points. Moreover, we discussed the parametric conditions for the existence of period-doubling bifurcations at their positive steady states for the discrete time system. Both types of bifurcations are verified by the Lyapunov exponents, while the maximum Lyapunov ensures chaotic and complex behaviour. Furthermore, in a three-dimensional discrete-time laser model, we used a hybrid control method to control period-doubling and Neimark-Sacker bifurcation. To validate our theoretical discussion, we provide some numerical simulations.

• 대한기계학회논문집A
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• 제30권2호
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• pp.194-201
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• 2006

Gait analysis is essential to identify accurate cause and knee condition from patients who display abnormal walking. Traditional linear tools can, however, mask the true structure of motor variability, since biomechanical data from a few strides during the gait have limitation to understanding the system. Therefore, it is necessary to propose a more precise dynamic method. The chaos analysis, a nonlinear technique, focuses on understand how variations in the gait pattern change over time. Eight healthy eight subjects walked on a treadmill for 100 seconds at 60 Hz. Three dimensional walking kinematic data were obtained using two cameras and KWON3D motion analyzer. The largest Lyapunov exponent from the measured knee angular displacement time series was calculated to quantify local stability. This study quantified the variability present in time series generated from gait parameter via chaos analysis. Knee flexion-extension patterns were found to be chaotic. The proposed Lyapunov exponent can be used in rehabilitation and diagnosis of recoverable patients.

• 한국정밀공학회지
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• 제23권2호
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• pp.164-171
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• 2006

Anterior cruciate ligament(ACL) injury of the knee is common and a serious ACL injury leads to ligament reconstruction surgery. Gait analysis is used to identify the result of surgery. The purpose of this study is to numerically evaluate and classify knee condition of patients through the chaos analysis. Experiments were carried out for 13 subjects (8 healthy subjects, 5 ACL deficient patients) walking on a treadmill. Sagittal kinematic data of the right lower extremity were collected by using a 3D motion analysis system. The recorded gait patterns were digitized and then coordinated by KWON3D. The largest Lyapunov exponent from the measured knee angular displacement time series was calculated to quantify local stability. It was found that the Lyapunov exponent becomes larger as the knee condition becomes worse. This study suggested a method of the severity of injury and the level of recovery. The proposed method discerns difference between healthy subjects and patients.