• Journal of Institute of Control, Robotics and Systems
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• v.14 no.7
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• pp.615-623
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• 2008

This paper proposes an $H_{\infty}$ controller design method for Takagi-Sugeno (T-S) fuzzy systems using a fuzzy basis-function-dependent Lyapunov function. Sufficient conditions for the guaranteed $H_{\infty}$ performance of the T-S fuzzy control system are given in terms of linear matrix inequalities (LMIs). These LMI conditions are further used for a convex optimization problem in which the $H_{\infty}-norm$ of the closed-loop system is to be minimized. To facilitate the basis-function-dependent Lyapunov function approach and thus improve the closed-loop system performance, additional decision variables are introduced in the optimization problem, which provide an additional degree-of-freedom and thus can enlarge the solution space of the problem. Numerical examples show the effectiveness of the proposed method.

• Journal of the Korean Institute of Intelligent Systems
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• v.27 no.1
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• pp.59-64
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• 2017

In this paper, a controller for discrete Takagi-Sugeno(T-S) fuzzy model under imperfect premise matching is proposed. Most of previous papers have obtained the stabilization condition using common quadratic Lyapunov function. However, the stabilization condition may be conservative due to the typical disadvantage of the common quadratic Lyapunov function. Hence, in order to solve this problem, we propose the stabilization condition of discrete T-S fuzzy model using fuzzy Lyapunov function. Finally, the proposed approach is verified by the simulation experiments.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.805-821
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• 2000

The paper deals with asymtotic stabillity of nonlinear nonautinomous systems by Lyapunov's direct method. The proposed Lyapunov-like function V(t, x) needs not be continuous in t and Lipschitz in x in a Banach space. The class of systems considered is allowed to be nonautonomous and infinite-dimensional and we relax the boundedness, the Lipschitz assumption on the system and the definite decrescent condition on the Lyapunov function.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.155-163
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• 2002

The purpose of this paper is to establish discrete versions of the well-known Lyapunov's stability theorem and LaSalle's invariance theorem for a non-autonomous discrete dynamical system. Our proofs for these theorems are constructive in the sense that they are made by explicitly building a Lyapunov function for the system. A comparison between non-autonomous discrete dynamical systems and continuous dynamical systems is conducted.

• Proceedings of the KIEE Conference
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• 1995.11a
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• pp.195-198
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• 1995

Most of the theorems of nonlinear stability is based on the Lyapunov stability theory. The Lyapunov function method is the most well-known and provides precise and rigorous theoretical backgrounds. However, tile conventional approach to direct stability analysis has been performed without taking account of damping effects. For accurate stability analysis of nonlinear systems, it is required to consider the damping effects. This paper presents a new method to derive a group of Lyapunov functions to reflect the damping effects by considering the integral relationships of the system governing equations. This method tan be utilized as a powerful tool to determine the region of attraction.

• Proceedings of the KIEE Conference
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• 2003.11b
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• pp.315-318
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• 2003

This paper proposes a switching control method applicable to any affine, 2nd order nonlinear system with single input. The key contribution is to develop a control design method which uses a piecewise continuous Lyapunov function non-increasing at every discontinuous point. The proposed design method requires no restrictions except full state availability. To obtain a non-increasing, piecewise continuous Lyapunov function, we change the sign of off-diagonal term s of the positive definite matrix composing the former Lyapunov function according to the sign of the Inter-connection term. And we use the solution of inequalities which guarantee each Lyapunov function is non-increasing at any discontinuous point.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.04a
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• pp.133-136
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• 2004

This paper proposes a stability condition in 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).

• Journal of Power Electronics
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• v.17 no.4
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• pp.983-990
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• 2017

This paper proposes a model predictive control based on the discrete Lyapunov function to improve the performance of power electronic converters. The proposed control technique, based on the finite control set model predictive control (FCS-MPC), defines a cost function for the control law which is determined under the Lyapunov stability theorem with a control error compensation. The steady state and dynamic performance of the proposed control strategy has been tested under a single phase AC/DC voltage source rectifier (S-VSR). Experimental results demonstrate that the proposed control strategy not only offers global stability and good robustness but also leads to a high quality sinusoidal current with a reasonably low total harmonic distortion (THD) and a fast dynamic response under linear loads.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.6
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• pp.548-553
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• 2008

In this paper, we propose a new swing-up control strategy for rotary inverted pendulums with restricted rotation range. The control law is derived from a Lyapunov function. The Lyapunov function is defined as the square of the sum of the absolute value of the total mechanical energy and weighted squares of the arm's angular displacement and velocity. By adjusting the weighting parameters in the Lyapunov function, we can affect the swing-up strategy such that the restriction on rotation range can be satisfied. Finally, we verify the performance of the proposed control law through simulation and experiments.

• Journal of Mechanical Science and Technology
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• v.14 no.11
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• pp.1225-1231
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• 2000

This paper proposes a V-shaped Lyapunov function approach for the model-based control of flexible-joint robots, in which a new model-based nonlinear control scheme is designed based on a V-shaped Lyapunov function. The proposed control guarantees global asymptotic stability for link trajectory control while keeping all internal signals bounded. Since joint flexibility is used as a control parameter, the proposed control is not restricted by the degree of joint flexibility and be applied to flexibility-joint, partly-flexibility, or rigid-joint robots without modification. the effectiveness of the proposed control has been by computer simulation.