• The Journal of Korean Institute of Communications and Information Sciences
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• v.17 no.12
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• pp.1333-1342
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• 1992

This paper deals with a robot manipulator having actuator which is described by equation $D(q)\ddot{q}=u-P(q\;\dot{q},\;\ddot{q})$ where u(t) is a control input. We employ two steps of controller design procedures. First, a global linearization is performed to yield a decoupled controllable linear system. Then a controller is designed for this linear system. We provide a rigorous analysis of the effect of uncertainty of the dynamics, which we study using robustness results in time domain based on a Lyapunov equation and the total stability theorem. Using this approach we simulate the performance of controller of a robot manipulator.

• International Journal of Control, Automation, and Systems
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• v.2 no.1
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• pp.55-67
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• 2004

In this paper, an active vibration control of a translating steel strip in a zinc galvanizing line is investigated. The control objectives in the galvanizing line are to improve the uniformity of the zinc deposit on the strip surfaces and to reduce the zinc consumption. The translating steel strip is modeled as a moving belt equation by using Hamilton’s principle for systems with moving mass. The total mechanical energy of the strip is considered to be a Lyapunov function candidate. A nonlinear boundary control law that assures the exponential stability of the closed loop system is derived. The existence of a closed-loop solution is shown by proving that the closed-loop dynamics is dissipative. Simulation results are provided.

• Transactions on Control, Automation and Systems Engineering
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• v.2 no.4
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• pp.235-243
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• 2000

The probabilistic data association filter(PDAF) is known to provide better tracking performance than the standard Kalman filter(KF) in a cluttered environment. In this paper, the stability of the PDAF of Fortmann et al[7], in the presence of uncertainties with regard to the origin of measurement, is investigated. The modified Riccati equation derived by approximating two random terms with their expectations is used to prove the stability of the PDAF. A new Lyapunov function based approach, which is different from the quantitative evaluation of Li and Bar-Shalom[7], is pursued. With the assumption that the system and observation noises are bounded, specific tracking error bounds are established.

• Journal of Institute of Control, Robotics and Systems
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• v.18 no.6
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• pp.513-518
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• 2012

In this paper, we propose a generalized index independent stability condition for a descriptor systemwithout any transformations of system matrices. First, the generalized Lyapunov equation with a specific right-handed matrix form is considered. Furthermore, the existence theorem and the necessary and sufficient conditions for asymptotically stable descriptor systems are presented. Finally, some suitable examples are used to show the validity of the proposed method.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.743-750
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• 2009

A class of Hermitian operators B admitting a positive semidefinite solution of the linear operator equation ${\sum}^n_{j=1}A^{n-j}XA^{j-1}=B$ for a fixed positive definite operator A is given via the Furuta inequality.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.741-748
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• 2012

In this work, we prove the instability of solutions for a class of nonlinear functional differential equations of the eighth order with n-deviating arguments. We employ the functional Lyapunov approach and the Krasovskii criteria to prove the main results. The obtained results extend some existing results in the literature.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.261-272
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• 2005

In this paper, boundedness criteria are established for solutions of a class of impulsive functional differential equations with infinite delays of the form $x'(t) = F(t, x(\cdot)), t > t^{\ast} {\Delta}x(t_{k})= I(t_{k}, x(t_{k}^{-})), k = 1,2,...$ By using Lyapunov functions and Razumikhin technique, some new Razumikhin-type theorems on boundedness are obtained.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.4
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• pp.445-468
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• 2020

A long-time behavior of global solutions for a dispersive-dissipative equation with time-dependent damping terms is investigated under null Dirichlet boundary condition. By virtue of an appropriate new Lyapunov function and the Lojasiewicz-Simon inequality, we show that any global bounded solution converges to a steady state and get the rate of convergence as well, when damping coefficients are integrally positive and positive-negative, respectively. Moreover, under the assumptions on on-off or sign-changing damping, we derive an asymptotic stability of solutions.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.907-914
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• 2015

In this paper, we consider a viscoelastic plate equation with p-Laplacian $u^{{\prime}{\prime}}+{\Delta}^2u-div({\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)+{\sigma}(t){\int}_{0}^{t}g(t-s){\Delta}u(s)ds-{\Delta}u^{\prime}=0$. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of both ${\sigma}$ and g.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1457-1470
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• 2017

In this paper, we consider the stabilization of the viscoelastic wave equation with variable coefficients in a bounded domain with smooth boundary, subject to linear dissipative internal feedback with a delay. Our stabilization result is mainly based on the use of the Riemannian geometry methods and Lyapunov functional techniques.