• Journal of the Korea Institute of Information and Communication Engineering
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• v.13 no.8
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• pp.1647-1652
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• 2009

Generally the neural network and the fuzzy compensative algorithm are applied to forecast the time series for power demand with a characteristic of non-linear dynamic system, but it has a few prediction errors relatively. It also makes long term forecast difficult for sensitivity on the initial condition. On this paper, we evaluate the chaotic characteristic of electrical power demand with analysis methods of qualitative and quantitative and perform a forecast simulation of electrical power demand in regular sequence, attractor reconstruction, time series forecast for multi dimension using Lyapunov exponent quantitatively. We compare simulated results with the previous method and verify that the purpose one being more practice and effective than it.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.5
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• pp.411-418
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• 2006

There are mainly two types of bang-bang controllers for nominal linear time-invariant (LTI) system. Optimal bang-bang controller is designed based on optimal control theory and suboptimal bang-bang controller is obtained by using Lyapunov stability condition. In this paper, the suboptimal bang-bang control method is extended to LTI system involving both control input saturation and structured real parameter uncertainties by using Lyapunov robust stability condition. Two robust optimal bang-bang controllers are derived by minimizing the time derivative of Lyapunov function subjected to the limit of control input. The one is developed based on the classical quadratic stability(QS), and the other is developed based on the affine quadratic stability(AQS). And characteristics of the two controllers are compared. Especially, bounds of parameter uncertainties which theoretically guarantee robust stability of the two controllers are compared quantitatively for 1DOF vibrating system. Moreover, the validity of robust optimal bang-bang controller based on the AQS is shown through numerical simulations for this system.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2009.05a
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• pp.171-174
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• 2009

Generally the neural network and the fuzzy compensative algorithm are applied to forecast the time series for power demand with a characteristic of non-linear dynamic system, but it has a few prediction errors relatively. It also makes long term forecast difficult for sensitivity on the initial condition. On this paper, we evaluate the chaotic characteristic of electrical power demand with analysis methods of qualitative and quantitative and perform a forecast simulation of electrical power demand in regular sequence, attractor reconstruction, time series forecast for multi dimension using Lyapunov exponent quantitatively. We compare simulated results with the previous method and verify that the purpose one being more practice and effective than it.

• IEMEK Journal of Embedded Systems and Applications
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• v.16 no.4
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• pp.119-127
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• 2021

The aim of this paper is to propose a less conservative stabilization condition for leader-following sampled-data control of wheeled mobile robot (WMR) systems by using a clock-dependent Lyapunov function (CDLF) with looped functionals. In the leader-following WMR system, the state and input of the leader robot are measured by digital devices mounted on the following robot, and they are utilized to construct the sampled-data controller of the following robot. To design the sampled-data controller, a stabilization condition is derived by using the CDLF with looped functionals, and formulated in terms of sum of squares (SOS). The considered Lyapunov function is a polynomial form with respect to the clock related to the transmitted sampling instants. As the degree of the Lyapunov function increases, the stabilization condition becomes less conservative. This ensures that the designed controller is able to stabilize the system with a larger maximum sampling interval. The simulation results are provided to demonstrate the effectiveness of the proposed method.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.155-158
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• 1997

In this paper, we present new results concerning the relationship between the input-output and Lyapunov stability of nonlinear system possessing a periodic orbit. Definition of small-signal finite-gain L$\sub$p/ stability around periodic orbit is introduced. We show L$\sub$p/ stability of exponentially stable periodic orbit using quadratic Lyapunov functions for the periodic orbit. The L$\sub$2/ gain analysis is presented with Hamiltonian-Jacobi inequality along with an example.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1844-1847
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• 1997

Assuming that EEG(electroencephalogram), which is generated by a nonlinear electrical of billions of neurons in the brain, has chaotic characteristics, it is confirmend by frequency spectrum analysis, log frequency spectrum analysis, correlation dimension analysis and Lyapunov exponents analysis. Some chaotic characteristics are related to the degree of brain activity. The slope of log frequency spectrum increases and the correlation dimension decreasess with respect to the activities, while the largest Lyapunov exponent has only a rough correlation.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.589-597
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• 2012

In this paper we investigate the stability of solutions of the perturbed differential equations with the positive order of the perturbation by using the notion of the Lyapunov exponent of unperturbed equations and an integral inequality of Bihari type.

• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.665-676
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• 2004

In this paper we characterize asymptotic stability via Lyapunov function in general dynamical systems on c-first countable space. We give a family of examples which have first countable but not c-first countable, also c-first countable and locally compact space but not metric space. We obtain several necessary and sufficient conditions for a compact subset M of the phase space X to be asymptotic stability.

• Proceedings of the KIEE Conference
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• 2003.11b
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• pp.131-134
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• 2003

In this paper, we consider the problem of finding the stability region in state space for uncertain linear systems with input saturation. For stability analysis, two Lyapunov functions are chosen. One is for the lineal region and the other is for the saturated legion. Piecewise Lyapunov functions are obtained by solving successive linear matrix inequalites(LMIs) relaxations. A sufficient condition for robust stability is derived in the form of stability region of initial conditions. A numerical example shows the effectiveness of the proposed method.

• The Transactions of the Korean Institute of Electrical Engineers P
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• v.53 no.4
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• pp.201-204
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• 2004

In this paper, a direct adaptive tracking controller based Lyapunov method is designed for a wheeled mobile robots. A wheeled mobile robots have three degrees of freedom and two control variables. Therefore, it is difficult to control a mobile robot using the general linear control. We introduce two kinds of Lyapunov function for the design of the controller and verify the controller. A mobile robots using the designed adaptive direct tracking controller is well-behaved and is easily implemented.