• Journal of the Korean Society of Manufacturing Process Engineers
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• v.20 no.4
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• pp.66-72
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• 2021

Since the behavior of an autonomous underwater vehicle (AUV) is influenced by disturbances and moments that are not accurately known, the depth control law of AUVs must have the ability to track the input signal and to reject disturbances simultaneously. Here, we proposed robust tracking control for controlling the depth of an AUV. An augmented closed-loop system is represented by an error dynamic equation, and we can easily show the asymptotic stability of the overall system by using a Lyapunov function. The robust tracking controller is consisted of the internal model of the command signal and a state feedback controller, and it has the ability to track the input signal and reject disturbances. The closed-loop control system is robust to parameter uncertainties. Simulation results showed the control performance of the robust tracking controller to be better than that of a P + PD controller.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.449-451
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• 2003

In this paper, the stability problem for singular bilinear system is investigated. We present state feedback control laws for two classes of singular bilinear plants. Asymptotic stability of the closed-loop systems is derived by employing singular Lyapunov's direct method. The primary advantage of our approach lies in its simplicity. In order to verify effectiveness of the results, two numerical examples are given.

• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.1
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• pp.46-51
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• 1987

Using the computer-generated Lyapunov functions due to Brayton-tong's constructive algorithm, we estimate the domains of attraction of dynamical systems of the second order, and analyze the asymptotic stability of large scale contincous-time and discrete-time systems by the decomposition and aggregation method. With this approach we get the less conservative stability results than the existing methods.

• Bulletin of the Korean Mathematical Society
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• v.34 no.4
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• pp.561-571
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• 1997

The general (continuous) solution and the asymptotic behaviors of the unbounded solution of the functional equation $f(x + y)^2 = af(x)f(y) + bf(x)^2 + cf(y)^2$ and the Hyers-Ulam stability of that functional equation for the case when a = 2 and b = c = 1 shall be investigated.

• Proceedings of the KIEE Conference
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• 2000.07d
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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.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.801-813
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• 2019

In this paper, using the Baire category theorem we investigate the Hyers-Ulam stability problem of pexiderized Jensen functional equation $$2f(\frac{x+y}{2})-g(x)-h(y)=0$$ and pexiderized Jensen type functional equations $$f(x+y)+g(x-y)-2h(x)=0,\\f(x+y)-g(x-y)-2h(y)=0$$ on a set of Lebesgue measure zero. As a consequence, we obtain asymptotic behaviors of the functional equations.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.539-553
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• 2011

We study the solvability of a perturbed quadratic functional-integral equation of fractional order with linear modification of the argument. This equation is considered in the Banach space of real functions defined, bounded and continuous on an unbounded interval. Moreover, we will obtain some asymptotic characterization of solutions.

• Journal of Korea Society of Industrial Information Systems
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• v.7 no.1
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• pp.75-80
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• 2002

We investigate sorry: asymptotic stabilities of the zero solution for the perturbed linear differential system dx/dt=A(t)x+e(t, x)+f(t,x), by using Perron's method and integral inequalities, etc. and we also find some sufficient conditions that ensure some asymptotic stabilities of the zero solution of the system And hence we obtain several results of it.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.3
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• pp.563-567
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• 2017

This paper deals with the depth and speed controls of a class of nonlinear large diameter unmanned underwater vehicles (LDUUVs), while maintaining its attitude. The concerned control problem can be viewed as an asymptotic stabilization of the error model in terms of its desired depth, surge speed and attitude. To tackle its nonlinearities, the linear parameter varying (LPV) model is employed. Sufficient linear matrix inequality (LMI) conditions are provided for its asymptotic stabilization. A numerical simulation is provided to demonstrate the effectiveness of the proposed design methodology.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.2
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• pp.409-415
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• 2017

This paper addresses on an linear matrix inequality (LMI) formulation of the robust waypoint tracking problem of large diameter unmanned underwater vehicles (LDUUVs) in the horizontal plane. The interested design issue can be reformed as the robust asymptotic stabilization of the provided error dynamics with respect to the desired yaw angle, surge speed and attitude. Sufficient conditions for its robust asymptotic stabilizability against the hydrodynamic uncertainties are derived in the format of LMI. An example is provided to testify the validity of the proposed theoretical claims.