• 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.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.4-4
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• 2000

In this paper, the backstepping control method that is useful for cascade systems is applied to the slew maneuver of the spacecraft. The quaternion is used for representing the attitude of the spacecraft, because the reference trajectory of angular velocity has simple mathematical form. The conventional backstepping control has severa] problems such as slow convergence, trivial cancelling of nonlinear terms, and excessive control input. To overcome these problems, the modified backstepping control method which is redesign of Lyapunov function is proposed. To design a tracking function for angular velocity, it is necessary to estimate the process of maximum angular velocity, and therefore the estimation procedure using Bellman-Gronwall inequality is developed. To verify the effectiveness of the proposed control law, numerical simulation is performed and the results are compared with the exiting control scheme.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.10
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• pp.109-117
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• 1999

In this paper, a direct adaptive control, based on Lyapunov Function Candidate, is applied to a nonlinear Gunner's Primary Stabilized Head Mirror system to derive a parameter adaptation scheme; furthemore, a nonlinear sliding mode control, but also compensating the error in identification of the parameters which are even varying of have uncertain values. The performance of the adaptive controller is determined by the tracking ability to a desired model under some disturbances and the slowly varying parameters of the system. Both adaptive scheme and sliding mode play an important fole in the improvement of the nonlinear system control.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.4
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• pp.317-335
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• 2014

In this work, we investigate the global stability analysis of a viral infection model with antibody immune response. The incidence rate is given by a general function of the populations of the uninfected target cells, infected cells and free viruses. The model has been incorporated with two types of intracellular distributed time delays to describe the time required for viral contacting an uninfected cell and releasing new infectious viruses. We have established a set of conditions on the general incidence rate function and determined two threshold parameters $R_0$ (the basic infection reproduction number) and $R_1$ (the antibody immune response activation number) which are sufficient to determine the global dynamics of the model. The global asymptotic stability of the equilibria of the model has been proven by using Lyapunov theory and applying LaSalle's invariance principle.

• Proceedings of the KIEE Conference
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• 1998.07b
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• pp.641-643
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• 1998

This paper deals with the stability of discrete time linear systems with time - varying delays in state. In this paper, the magnitude of time - varying delays is assumed to be upper-bounded. The stability of discrete time linear systems with time - varying delays in state is related with the stability of discrete time linear systems with constant time delay in state. To show this, a new Lyapunov function is proposed. Using this Lyapunov function, a sufficient condition for the asymptotic stability is derived.

• Journal of Institute of Control, Robotics and Systems
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• v.16 no.3
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• pp.239-244
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• 2010

This paper is to present map building of mobile robot using RFID (Radio Frequency Identification) technology and ultrasonic sensor. For mobile robot to perform map building, the mobile robot needs its localization and accurate driving in space. In this reason, firstly, kinematic modeling of mobile robot under non-holonomic constrains is introduced. Secondly, based on this modeling, a tracking controller is designed for tracking a given path based on backstepping method using Lyapunov function. The Lyapunov function is also introduced for proving the stability of the designed tracking controller. Thirdly, 2D map building is performed by RFID system, mobile robot system and ultrasonic sensors. The RFID mobile robot system is composed of DC motor, encoder, ultra sonic sensor, digital compass, RFID receiver and RFID antenna. Finally, the path tracking simulation results and map building experimental results are presented to show the effectiveness of the designed controller.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.52 no.7
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• pp.385-392
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• 2003

A nonlinear speed controller for a separately excited DC motor (SEDCM) based on a newly developed adaptive backstepping approach is presented. To compensate parameter uncertainties and load torque disturbance, a nonlinear adaptive backstepping control law and adaptive law are derived systematically step by step through virtual control input and suitable Lyapunov function. Also, speed observer without using costly speed sensor is presented. Simulation results show that the proposed controller can observe real speed and track the reference speed signal generated by a reference model.

• Proceedings of the KIEE Conference
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• 1998.07c
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• pp.982-984
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• 1998

In this paper, a stability proof of the closed-loop stability for the nonlinear feedback linearization-$H_\infty$/sliding mode controller (NFL-$H_\infty$/SMC) is done by a Lyapunov function candidate using an addition form of the sliding surface vector and the estimation error.

• Proceedings of the KIEE Conference
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• 1998.07c
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• pp.994-996
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• 1998

In this paper, the standard Dole, Glover, Khargoneker, and Francis (abbr. : DGKF 1989) $H_{\infty}$ controller $(H_{\infty}C)$ is extended to the nonlinear feedback linearization-$H_\infty$-based sliding mode controller (NFL-$H_\infty$-based SMC). A stability proof of the closed-loop stability is done by a Lyapunov function candidate using an addition form of the sliding surface vector and the estimation error.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.6
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• pp.581-588
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• 2007

In this paper, we propose a delayed feedback guaranteed cost controller design method for linear time-delay systems with norm-bounded parameter uncertainties and nonlinear perturbations. A quadratic cost function is considered as the performance measure for the given system. Based on the Lyapunov method, an LMI optimization problem is formulated to design a controller such that the closed-loop cost function value is not more than a specified upper bound for all admissible system uncertainties and nonlinear perturbations. Numerical example show the effectiveness of the proposed method.