• 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.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.51 no.2
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• pp.43-47
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• 2002

Stability conditions of time-varying discrete state delay systems are proposed. The time-varying state delay is assumed that (i) the magnitude is known to lie in a certain interval (ii) the upper bound of the rate of change is known. Under these conditions, new stability conditions are derived based on switched Lyapunov functions. Stability conditions for both fast time-varying and slowly time-varying delay are considered.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.7
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• pp.523-528
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• 2000

In this short note the characteristics of a nonlinear system of which the state trajectories are oscillating in the phase plane are overviewed. The physical concept of stuck and sliding patch phenomena are also introduced by adding some switching functions and their stability on the sliding patches are analyzed by using the Lyapunov stability theory and Frobenius theorem.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.658-662
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• 2004

This paper develops a stability analysis and controller synthesis methodology for a continuous-time affine Takagi-Sugeno (T-S) fuzzy systems with parametric uncertainties. Affine T-S fuzzy system can be an advantage because it may be able to approximate nonlinear functions to high accuracy with fewer rules than the homogeneous T-S fuzzy systems with linear consequents only. The analysis is based on Lyapunov functions that are continuous and piecewise quadratic. The search for a piecewise quadratic Lyapunov function can be represented in terms of bilinear matrix inequalities (BMIs). A simulation example is given to illustrate the application of the proposed method.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.869-878
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• 2013

We study boundedness of solutions of dynamic equations on time scales by using Lyapunov-type functions.

• Proceedings of the KIEE Conference
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• 2004.07d
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• pp.2516-2518
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• 2004

This paper proposes a stability condition in discrete-time affine Takagi-Sugeno (T-S) fuzzy systems with parametric uncertainties and then, introduces the design method of a fuzzy-model-based controller which guarantees the stability. The analysis is based on Lyapunov functions that are continuous and piecewise quadratic. The search for a piecewise quadratic Lyapunov function can be represented in terms of linear matrix inequalities (LMIs).

• Earthquakes and Structures
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• v.21 no.6
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• pp.577-585
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• 2021

In this research, a neural network (NN) method was developed, which combines H-infinity and fuzzy control for the purpose of stabilization and stability analysis of nonlinear systems. The H-infinity criterion is derived from the Lyapunov fuzzy method, and it is defined as a fuzzy combination of quadratic Lyapunov functions. Based on the stability criterion, the nonlinear system is guaranteed to be stable, so it is transformed to be a linear matrix inequality (LMI) problem. Since the demo active vibration control system to the tuning of the algorithm sequence developed a controller in a manner, it could effectively improve the control performance, by reducing the wind's excitation configuration in response to increase in the cost efficiency, and the control actuator.

• Journal of Korea Society of Industrial Information Systems
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• v.9 no.4
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• pp.75-79
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• 2004

We investigate various $\phi_0-boundedness$ and $\phi_0-Lagrange$ stability of the trivial solution of comparison differential system. We also investigated the corresponding boundedness concepts of the trivial solution of the differential system using the theory of differential inequalities through cones and the method of cone valued Lyapunov functions.

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.2
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• pp.112-124
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• 2004

A neural network based adaptive reconfigurable flight controller is presented for a class of discrete-time nonlinear flight systems in the presence of variations of aerodynamic coefficients and control effectiveness decrease caused by control surface damage. The proposed adaptive nonlinear controller is developed making use of the backstepping technique for the angle of attack, sideslip angle, and bank angle command following without two time separation assumption. Feedforward multilayer neural networks are implemented to guarantee reconfigurability for control surface damage as well as robustness to the aerodynamic uncertainties. The main feature of the proposed controller is that the adaptive controller is developed under the assumption that all of the nonlinear functions of the discrete-time flight system are not known accurately, whereas most previous works on flight system applications even in continuous time assume that only the nonlinear functions of fast dynamics are unknown. Neural networks learn through the recursive weight update rules that are derived from the discrete-time version of Lyapunov control theory. The boundness of the error states and neural networks weight estimation errors is also investigated by the discrete-time Lyapunov derivatives analysis. To show the effectiveness of the proposed control law, the approach is i]lustrated by applying to the nonlinear dynamic model of the high performance aircraft.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.4
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• pp.329-339
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• 2003

A neural network based adaptive controller design method is proposed for reconfigurable flight control systems in the presence of variations in aerodynamic coefficients or control effectiveness decrease caused by control surface damage. The neural network based adaptive nonlinear controller is developed by making use of the backstepping technique for command following of the angle of attack, sideslip angle, and bank angle. On-line teaming neural networks are implemented to guarantee reconfigurability and robustness to the uncertainties caused by aerodynamic coefficients variations. The main feature of the proposed controller is that the adaptive controller is designed with assumption that not any of the nonlinear functions of the system is known accurately, whereas most of the previous works assume that only some of the nonlinear functions are unknown. Neural networks loam through the weight update rules that are derived from the Lyapunov control theory. The closed-loop stability of the error states is also investigated according to the Lyapunov theory. A nonlinear dynamic model of an F-16 aircraft is used to demonstrate the effectiveness of the proposed control law.