• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.687-697
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• 2015

This paper shows that the solutions to the perturbed nonlinear functional differential system

• 제어로봇시스템학회:학술대회논문집
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• 1987.10a
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• pp.721-723
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• 1987

An Adaptation algorithm is presented and a convergence criterion is derived for parallel model reference adaptive bilinear systems. The output error converges asymptotically to zero, and the parameter estimates are bounded for stable reference models. The convergence criterion depends only upon the input sequence and a priori estimates of the maximum parameter values.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.797-804
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• 2010

The aim of this paper is to investigate the global stability, periodic nature, oscillation and the boundedness of solutions of the difference equation $x_{n+1}\;=\;\frac{A+Bx_{n-1}}{C+Dx_n^2}$, n = 0, 1, 2, ... where A, B are nonnegative real numbers and C, D > 0.

• 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.

• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.779-794
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• 2012

In this paper, we study the global stability of two mathematical models for human immunodeficiency virus (HIV) infection with intra-cellular delays. The first model is a 5-dimensional nonlinear delay ODEs that describes the interaction of the HIV with two classes of target cells, $CD4^+$ T cells and macrophages taking into account the saturation infection rate. The second model generalizes the first one by assuming that the infection rate is given by Beddington-DeAngelis functional response. Two time delays are used to describe the time periods between viral entry the two classes of target cells and the production of new virus particles. Lyapunov functionals are constructed and LaSalle-type theorem for delay differential equation is used to establish the global asymptotic stability of the uninfected and infected steady states of the HIV infection models. We have proven that if the basic reproduction number $R_0$ is less than unity, then the uninfected steady state is globally asymptotically stable, and if the infected steady state exists, then it is globally asymptotically stable for all time delays.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.11
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• pp.2139-2146
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• 2011

In this paper, a robust adaptive controller is proposed for trajectory tracking of robot manipulators with the unknown friction coefficient and bounded disturbance. A new adaptive control law is developed based on sliding mode and derived from the Lyapunov stability analysis. The introduction of a boundary layer solves the problem of chattering. The proposed adaptive controller is globally asymptotically stable and guarantees zero steady state error for joint positions. The estimated friction coefficients can also approach the actual coefficients asymptotically. A simulation example is provided to demonstrate the performance of the proposed algorithm.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.1 no.1
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• pp.44-49
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• 2001

For minimum phase systems, the conventional fuzzy logic controllers (FLCs) use the error and the change-of-error as fuzzy input variables. Then the control rule table is a skew symmetric type, that is, it has UNLP (Upper Negative and Lower Positive) or UPLN property. This property allowed to design a single-input FLC (SFLC) that has many advantages. But its control parameters are not automatically adjusted to the situation of the controlled plant. That is, the adaptability is still deficient. We here design a single-input direct adaptive FLC (SDAFLC). In the AFLC, some parameters of the membership functions characterizing the linguistic terms of the fuzzy rules are adjusted by an adaptive law. The SDAFLC is designed by a stable error dynamics. We prove that its closed-loop system is globally stable in the sense that all signals involved are bounded and its tracking error converges to zero asymptotically. We perform computer simulations using a nonlinear plant and compare the control performance between the SFLC and the SDAFLC.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.685-699
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• 2019

This research is focused on a continuous epidemic model of transmission of Plasmodium vivax malaria with a time delay. The model is represented as a system of ordinary differential equations with delay. There are two equilibria, which are the disease-free state and the endemic equilibrium, depending on the basic reproduction number, $R_0$, which is calculated and decreases with the time delay. Moreover, the disease-free equilibrium is locally asymptotically stable if $R_0<1$. If $R_0>1$, a unique endemic steady state exists and is locally stable. Furthermore, Hopf bifurcation is applied to determine the conditions for periodic solutions.

• Journal of Korea Water Resources Association
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• v.46 no.5
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• pp.491-504
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• 2013

In this study, wave breakings over a shelf region are investigated under irregular wave conditions through laboratory experiments in a wave flume. Numerical simulations based on the Boussinesq-type equations are also conducted. The characteristics of breaking waves such as significant wave height, crest and trough heights, the mean water level and the stable wave height are obtained by analyzing laboratory measurements in detail. Obtained results are compared with those of the Boussinesq-type equations model. A very reasonable agreements is observed. The broken waves over a horizontal bottom asymptotically approach a stable wave height($H_{stable}$). In this study, the relative stable wave height is found as $H_{stable}/h{\fallingdotseq}0.56$ for irregular wave.

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.439-445
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• 2007

The aim of this work is to investigate the global stability, periodic nature, oscillation and the boundedness of solutions of the difference equation $$x_{n+1}={\frac{Ax_{n-1}}{B+Cx_{n-2}{\iota}x_{n-2k}$$, n = 0, 1, 2,..., where A, B, C are nonnegative real numbers and $\iota$, k are nonnegative in tegers, $\iota{\leq}k$.