• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1921-1930
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• 2018

We consider a functional difference equation and use fixed point theory to obtain necessary and sufficient conditions for the asymptotic stability of its zero solution. At the end of the paper we apply our results to nonlinear Volterra infinite delay difference equations.

• International Journal of Aeronautical and Space Sciences
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• v.7 no.2
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• pp.1-13
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• 2006

The Lyapunov stability theory has been known inadequate to prove capturability of guidance laws because the equations of motion resulted from the guidance laws do not have the equilibrium point. By introducing a proper transformation of the range state, the original equations of motion for a stationary target can be converted into nonlinear equations with a specified equilibrium subspace. Physically, the equilibrium subspace denotes the direction of missile velocity to the target. By using a single Lyapunov function candidate, capturability of several PN laws for a stationary target is then proved for examples. In this approach, there is no assumption of the constant speed missile. The proposed method is expected to provide a unified and simplified scheme to prove the capturability of various kinds of guidance laws.

• International Journal of Aeronautical and Space Sciences
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• v.4 no.1
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• pp.99-109
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• 2003

Attitude control law synthesis for the three-axis attitude maneuver of a flexible spacecraft model is presented in this study. The basic idea is motivated by previous works for the extension into a more general case. The new case includes gravitational gradient torque which has significant effect on a wide range of low earth orbit missions. As the first step, the fully nonlinear dynamic equations of motion are derived including gravitational gradient. The control law design based upon the Lyapunov approach is attempted. The Lyapunov function consists of a weighted combination of system kinetic and potential energy. Then, a set of stabilizing control law is derived from the basic Lyapunov stability theory. The new control law is therefore in a general form partially validating the previous work in some sense.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.2
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• pp.96-101
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• 2007

Neural networks are known as kinds of intelligent strategies since they have learning capability. There are various their applications from intelligent control fields; however, their applications have limits from the point that the stability of the intelligent control systems is not usually guaranteed. In this paper we propose an adaptive tracking control for robot manipulators using the radial basis function network (RBFN) that is e. kind of neural networks. Adaptation laws for parameters of the RBFN are developed based on the Lyapunov stability theory to guarantee the stability of the overall control scheme. Filtered tracking errors between actual outputs and desired outputs are discussed in the sense of the uniformly ultimately boundedness(UUB). Additionally, it is also shown that parameters of the RBFN are bounded. Experimental results for a SCARA-type robot manipulator show that the proposed adaptive tracking controller is adaptable to the environment changes and is more robust than the conventional PID controller and the neuro-controller based on the multilayer perceptron.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.11
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• pp.2066-2073
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• 2008

In this paper, the problem of global asymptotic stability of uncertain stochastic neural networks with delay is considered. The delay is assumed to be time-varying and belong to a given interval. Based on the Lyapunov stability theory, new delay-dependent stability criteria for the system is derived in terms of LMI(linear matrix inequality). Three numerical examples are given to show the effectiveness of proposed method.

• Proceedings of the KIEE Conference
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• 1998.11b
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• pp.463-465
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• 1998

In this paper, we consider the problem of robust stability of large-scale uncertain linear systems with time-varying delays. The considered uncertainties are both unstructured uncertainty which is only known its norm bound and structured uncertainty which is known its structure. Based on Lyapunov stability theorem and $H_{\infty}$ theory. we present uncertainty upper bound that guarantee the robust stability of systems. Especially, robustness bound are obtained directly without solving the Lyapunov equation. Finally, we show the usefulness of our results by numerical example.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.30B no.3
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• pp.22-30
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• 1993

In this paper, robust adaptive control algorithms which can be applied to unknown uncertain systems are suggested. Transform matrix for dividing states into "uncontrolled" states and "controlled" states and general searching procedure for the transform matrix which assign arbitrary n-1 eigen values for the uncontrolled subsystem of n-th orther single-input single-output systems of which state variables can be observable are also studied and utilized for the design of new-type controllers. We drived new-type control laws by using adaptive control theory and variable structure system and its stability is proved by using Lyapunov stability theory.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.4
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• pp.88-96
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• 1997

This paper suggests a new non-linear friction compensation for digital control systems. This control adopts a hysteresis nonlinear element which can introduce the phase lead of the control system to compensate the phase delay comes from the inherent time delay of a digital control. A proper Lyapunov function is selected and the Lyapunov direct method is used to prove the asymptotic stability of the suggested control.

• The Journal of the Korea institute of electronic communication sciences
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• v.4 no.3
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• pp.236-242
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• 2009

When two-link flexible arm is rotated about an joint axis, transverse vibration may occur. In this paper, vibration dynamics of flexible robot arm is modeled by using Bernoulli-Euler beam theory and Lagrange equation. Using the fact that matrix $\dot{D}$-2C is skew symmetric, new controllers which have a simplified structure with less computational burden is proposed. Lyapunov stability theory is applied to achieve a stable deterministic nonlinear controller for the regulation of joint angle.

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.12
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• pp.1249-1255
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• 2004

A new parameter adaptation scheme for RBF Neural Network (NN) has been developed in this paper. Even though the RBF Neural Network (NN) based controllers are robust against both un-modeled dynamics and external disturbances, the performance is not satisfactory for a fast and precise mobile robot. To improve the tracking performance as well as robustness, all the parameters of RBF NN are updated in real time. The stability of this control law is rigorously proved by following the Lyapunov stability theory and shown by the experimental simulations. The fact that all of the weighting factors, width and center of RBF NN have been updated implies that this scheme utilizes all the possibilities in RBF NN to make the controller robust and precise while the mobile robot is following un-known trajectories. The performance of this new algorithm has been compared to the conventional RBF NN controller where some of the parameters are adjusted for robustness.