• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.05a
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• pp.315-318
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• 2003

A systematic output-tracking control design technique for robust control of Takagi-Sugeno (T-S) fuzzy systems with norm-bounded uncertainties is developed. The uncertain T-S fuzzy system is first represented as a set of uncertain local linear systems. The tracking problem is then converted into the stabilization problem for a set of uncertain local linear systems thereby leading to a more feasible controller design procedure. A sufficient condition for robust asymptotic output tracking is derived in terms of a set of linear matrix inequalities (LMIs). A stability condition on the traversing time-instances is also established. The output tracking control simulation for a flexible-joint robot-arm model is demonstrated, to convincingly show the effectiveness of the proposed system modeling and controller design method.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.144-149
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• 1993

This paper discusses a design of a nonlinear control for a class of single-input double-output nonlinear mechanical systems. When conventional linearization methods are applied to the mechanical systems, some problems of oscillation and unstable phenomena arise. The proposed nonlinear control system resolves these problems. In this design the eigenvalues of the closed-loop nonlinear system are assigned to desired locations and local asymptotic stability of the closed-loop system. is guaranteed. The design method is applied to an inverted pendulum system with a moving weight mechanism. Experimental results show that the proposed nonlinear controller is more effective for stability than the usual linear controller.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.267-276
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• 2017

The purpose of this paper is to investigate the local asymptotic stability of equilibria, the periodic nature of solutions, the existence of unbounded solutions and the global behavior of solutions of the fractional difference equation $$x_{n+1}=\frac{^{{\alpha}x}n-1(k+1)}{{\beta}+{\gamma}x^p_{n-k}x^q_{n-(k+2)}}$$, $$n=0,1,{\dots}$$ where the parameters ${\alpha}$, ${\beta}$, ${\gamma}$, p, q are non-negative numbers and the initial values $x_{-(k+2)}$,$x_{-(k+1)}$, ${\dots}$, $x_{-1}$, $x_0{\in}\mathb{R}^+$.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1385-1394
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• 2016

Let (R, m) be a Noetherian local ring, I, J two ideals of R, and A an Artinian R-module. Let $k{\geq}0$ be an integer and $r=Width_{>k}(I,A)$ the supremum of lengths of A-cosequences in dimension > k in I defined by Nhan-Hoang [9]. It is first shown that for each $t{\leq}r$ and each sequence $x_1,{\cdots},x_t$ which is an A-cosequence in dimension > k, the set $$\Large(\bigcup^{t}_{i=0}Att_R(0:_A(x_1^{n_1},{\ldots},x_i^{n_i})))_{{\geq}k}$$ is independent of the choice of $n_1,{\ldots},n_t$. Let r be the eventual value of $Width_{>k}(0:_AJ^n)$. Then our second result says that for each $t{\leq}r$ the set $\large(\bigcup\limits_{i=0}^{t}Att_R(Tor_i^R(R/I,\;(0:_AJ^n))))_{{\geq}k}$ is stable for large n.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.3
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• pp.151-167
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• 2012

In this paper, we investigate the dynamic behaviors of a one-prey and two-predator system with Holling-type II functional response and defensive ability by introducing a proportion that is periodic impulsive harvesting for all species and a constant periodic releasing, or immigrating, for predators at different fixed time. We establish conditions for the local stability and global asymptotic stability of prey-free periodic solutions by using Floquet theory for the impulsive equation, small amplitude perturbation skills. Also, we prove that the system is uniformly bounded and is permanent under some conditions via comparison techniques. By displaying bifurcation diagrams, we show that the system has complex dynamical aspects.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.107-121
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• 2023

An epidemic infectious disease model consists of six compartments viz. Susceptible, Exposed, Infected, Quarantine, Recovered, and Virus with nonlinear saturation incidence rate is proposed to know the viral disease dynamics. There exist two biological equilibrium points for the model system. The system's local and global stability is done through Lyapunov's direct method about equilibrium points. The sensitivity analysis has been performed for the basic reproduction number and equilibrium points through the normalized forward sensitivity index. Sensitivity analysis shows that virus growth and quarantine rates are more sensitive parameters. In support of mathematical conclusions, numerical experimentation has been shown.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.12
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• pp.1197-1204
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• 2008

This paper presents an asymptotic formation control scheme for a group of underactuated autonomous underwater vehicles (AUVs) where only three control inputs - surge force, yaw moment and pitch moment are available for each vehicle's six degree of freedom (DOF) underwater motion. Usually, the dynamics agents applied in most of the formation algorithms presented so far have been modeled as particle systems, which is a simple double-integrator system. Therefore, these algorithms cannot be directly applicable to the practical systems, especially to the underwater vehicles whose dynamics are highly nonlinear. Moreover, the vehicles considered in this paper are underactuated. The formation control is derived using general potential function method, and the corresponding potential function consists of two parts: interactions between vehicles and virtual-leader following. Proposed formation scheme guarantees asymptotic local stability of closed-loop system. Numerical simulations are carried out to illustrate the effectiveness of proposed formation scheme.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.747-767
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• 2013

In this paper we have constructed a mathematical model of alcohol abuse which consists of four compartments corresponding to four population classes, namely, moderate and occasional drinkers, heavy drinkers, drinkers in treatment and temporarily recovered class. Basic reproduction number $R_0$ has been determined and sensitivity analysis of $R_0$ indicates that ${\beta}1$ (the transmission coefficient from moderate and occasional drinker to heavy drinker) is the most useful parameter for preventing drinking habit. Stability analysis of the model is made using the basic reproduction number. The model is locally asymptotically stable at disease free or problem free equilibrium (DFE) $E_0$ when $R_0<1$. It is found that, when $R_0=1$, a backward bifurcation can occur and when $R_0>1$, the endemic equilibrium $E^*$ becomes stable. Further analysis gives the global asymptotic stability of DFE under some conditions. Our important analytical findings are illustrated through computer simulation. Epidemiological implications of our analytical findings are addressed critically.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.531-540
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• 2015

Let (R, m) be a Noetherian local ring, I an ideal of R, and A an Artinian R-module. Let $k{\geq}0$ be an integer and $r=Width_{>k}(I,A)$ the supremum of length of A-cosequence in dimension > k in I defined by Nhan-Hoang [8]. It is shown that for all $t{\leq}r$ the sets $$(\bigcup_{i=0}^{t}Att_R(Tor_i^R(R/I^n,A)))_{{\geq}k}\;and\\(\bigcup_{i=0}^{t}Att_R(Tor_i^R(R/(a_1^{n_1},{\cdots},a_l^{n_l}),A)))_{{\geq}k}$$ are independent of the choice of $n,n_1,{\cdots},n_l$ for any system of generators ($a_1,{\cdots},a_l$) of I.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.2
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• pp.185-190
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• 2005

A systematic output tracking control design technique for robust control of Takagi-Sugeno (T-S) fuzzy systems with norm bounded uncertainties is developed. The uncertain T-S fuzzy system is first represented as a set of uncertain local linear systems. The tracking problem is then converted into the stabilization problem for a set of uncertain local linear systems thereby leading to a more feasible controller design procedure. A sufficient condition for robust asymptotic output tracking is derived in terms of a set of linear matrix inequalities. A stability condition on the traversing time instances is also established. The output tracking control simulation for a flexible-joint robot-arm model is demonstrated, to convincingly show the effectiveness of the proposed system modeling and controller design.