• Journal of the Korean Society for Precision Engineering
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• v.22 no.4
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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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• v.29 no.5_6
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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.

• 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.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.2
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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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• v.15 no.1
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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.

• The Transactions of the Korean Institute of Power Electronics
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• v.4 no.2
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• pp.138-143
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• 1999

A new control method for the precision robust position control of a brushless DC(BLDC) motor for direct drive m motor(BLDDM) system using the asymptotically stable adaptive load torque observer is presented. A precision position c control is obtained for the BLDD motor system appro성mately linearized using the fieldlongrightarroworientation method. Many of t these motor systems have BLDD motor to obtain no backlashes. On the other hand, it has disadvantages such as the h high cost and more complex controller caused by the nonlinear characteristics. And the load torque disturbance is d directly affected to a motor shaft. To r밍ect this problem, stability analysis is calTied out using Lyapunov stability t theorem. Using this results, the stability is proved and load disturbance detected by the asymptotically stable adaptive observer is compensated by feedforwarding the equivalent CUlTent having the fast response.

• International Journal of Control, Automation, and Systems
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• v.4 no.4
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• pp.506-515
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• 2006

This paper studies an intelligent digital control for nonlinear systems with multirate sampling. It is worth noting that the multirate control design is addressed for a given nonlinear system represented by Takagi-Sugeno (T-S) fuzzy models. The main features of the proposed method are that i) it is provided that the sufficient conditions for stabilization of the discrete-time T-S fuzzy system in the sense of Lyapunov stability criterion, which is can be formulated in the linear matrix inequalities (LMIs); and ii) the stability properties of the trivial solution of the digital control system can be deduced from that of the solution of its discretized versions. An example is provided for showing the feasibility of the proposed method.

• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.169-172
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• 1999

In this paper, piecewise quadratic Lyapunov functions are used to analyze the stability of fuzzy-model-based controller. We represent the nonlinear system using a Takagi-Sugeno fuzzy model, which represent the given nonlinear system by fuzzy inference rules and local linear dynamic models. The proposed stability analysis technique is developed by dividing the whole fuzzy system into the smaller separate fuzry systems to reduce the conservatism. Some necessary and sufficient conditions for the proposed method are obtained. Finally, stability of the closed system with various kinds of controller for TS fuzzy model is checked through the proposed method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.2 s.245
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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.

• Journal of Institute of Control, Robotics and Systems
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• v.15 no.1
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• pp.72-81
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• 2009

This paper presents a robust adaptive control method using model reference control strategy against autonomous robot systems with random friction nature. We approximate a nonlinear robot system model by means of a feedback linearization approach to derive nominal control law. We construct a Least Square (LS) based observer to estimate friction dynamics online and then represent a perturbed system model with respect to approximation error between an actual friction and its estimation. Model reference based control design is achieved to implement an auxiliary control in order for reducing control error in practice due to system perturbation. Additionally, we conduct theoretical study to demonstrate stability of the perturbed system model through Lyapunov theory. Numerical simulation is carried out for evaluating the proposed control methodology and demonstrating its superiority by comparing it to a traditional nominal control method.