• Proceedings of the KIEE Conference
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• 1993.07a
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• pp.106-108
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• 1993

This paper gives derivations of voltage collapse conditions by using the Lyapunov function, which yields the exactly same results with the sensitivity analysis approach. On the other hand, the voltage collapse phenomenon is interpreted in the physical sense, and causes of the static voltage unstability and the dynamic voltage unstability are analyzed with the use of proposed Lyapunov function. In addition a new method is developed to calculate the power capacity limit of transmission lines with respect to voltage stability. This paper shows that it is able to analyze the voltage collapse with the Lyapunov direct method in the simple 2-bus system and proposes that the method works well by observing the variation of Lyapunov function as the load is increased in the system.

• 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.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.12-12
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• 2000

This paper consider a new weighted model reduction using block diagonal solutions of Lyapunov inequalities. With the input and/or output weighting function, the stability of reduced order system is quaranteed and a priori error bound is proposed. to achieve this, after finding the solutions of two Lyapunov inequalities and balancing the full order system, we find the reduced order systems using the direct truncation and the singular perturbation approximation. The proposed method is compared with other existing methods using numerical example.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.6
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• pp.477-486
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• 2001

Many physical systems can be modeled by incorporating continuous and discrete event nature together. Such hybrid systems contain both continuous and discrete states that influence the dynamic be-havior of the systems. There has been an increasing interest in thers types of systems during the last dec-ade, mostly due to the growing usage of computers in the control of physical plants but also as a result of the hybrid nature of physical processes. The stability theory for hybrid systems is considered as extension of Lyapunov theory where the existence of an abstract energy function satisfying certain properties verifies stability, called multiple Lyapunov theory. In this paper, a hybrid stabilizing controller is proposed using the control Lyapunov function method and multiple Lyapunov theory, and the proposed method is applied to lon-gitudinal spacing control in a vehicle platoon for intelligent transportation systems(ITS).

• The Journal of the Acoustical Society of Korea
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• v.16 no.4
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• pp.42-48
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• 1997

This paper has apparaised ability of speaker recognition and speech recognition using correlation dimension and Lyapunov dimension. In this method, speech was regarded the cahos that the random signal is appeared in determinisitic raising system. we deduced exact correlation dimension and Lyapunov dimension with searching important orbit from AR model power spectrum when reconstruct strange attractor using Taken's embedding theory. We considered a usefulness of speech recognition and speaker recognition using correlation dimension and Lyapunov dimension that characterized reconstruction attractor. As a result of consideration, which were of use more the speaker recognition than speech recognition, and in case of speaker recognition using Lyapunov dimension were much recognition rate more than speaker recognitions using correlation dimension.

• Journal of Electrical Engineering and information Science
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• v.3 no.3
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• pp.322-329
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• 1998

Stability analysis of nonlinear systems is mostly based on the Lyapunov stability theory. The well-known Lyapunov function method provides precise and rigorous theoretical backgrounds. However, the conventional approach to direct stability analysis has been performed without taking account of damping effects, which is pointed as a minor but crucial drawback. For accurate has been performed without taking account of damping effects, which is pointed as a minor but crucial drawback. For accurate stability analysis of nonlinear systems, it is required to take the damping effects into account. 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. A systematical approach is developed to convert a part of damping loss into some appropriate system energy terms. Examples show that the proposed method remarkably improves the estimation of the region of attraction compared considering damping effects. The proposed method can be utilized as a useful tol to determine the region of attraction.

• The Transactions of the Korean Institute of Electrical Engineers P
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• v.61 no.4
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• pp.161-167
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• 2012

Energy conversion systems such as power inverters and converters are basically significant in establishing photovoltaic power systems to enhance power effectiveness. This paper proposes a new converter control method by using the Lyapunov redesign approach. We construct the proposed control mechanism linearly composed of nominal control and auxiliary control laws. The former is generally designed through a well-known power electronic technology and the latter is implemented to compensate real-time control error due to uncertain natures of converter systems in practice. For realizing adaptive control capability in the proposed control mechanism, a control parameter vector is estimated by utilizing a steepest descent based optimization method. We carry out numerical simulation with Matlab(c) software to demonstrate reliability of the proposed converter control system and conduct a comparative study to prove its superiority by comparing with a generic converter control methodology.

• 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 Institute of Control, Robotics and Systems
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• v.7 no.6
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• pp.465-470
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• 2001

This paper considers a new weighed model reduction method using block diagonal solutions of Lyapunov inequalities. With the input and/or output weighting function, the stability of the reduced order system is guaranteed and an a priori error bound is proposed. to achieve this after finding the solutions of two Lyapunov inequalities and balancing the full order system, we find the reduced order systems using the direct truncation and the singular perturbation approximation. The proposed method is compared with other existing methods using numerical examples.

• KIEE International Transaction on Systems and Control
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• v.2D no.2
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• pp.97-107
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• 2002

In this paper, we propose the concept of orthonormalized compressed measurement for the stability analysis of discrete linear time-varying Kalman filters. Unlike previous studies that deal with the homogeneous portion of Kalman filters, the proposed Lyapunov method directly deals with the stochastically-driven system. The orthonorrmalized compressed measurement provides information on the a priori state estimate of the Kalman filter at the k-th step that is propagated from the a posteriori state estimate at the previous block of time. Since the complex multiple-step propagations of a candidate Lyapunov function with process and measurement noises can be simplified to a one-step Lyapunov propagation by the orthonormalized compressed measurement, a stochastic radius of attraction can be derived that would be impractically difficult to obtain by the conventional multiple-step Lyapunov method.