• 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.

• Journal of the Korean Mathematical Society
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• v.36 no.2
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• pp.403-419
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• 1999

We introduce a Hamiltonian system which consists of two balls in the vertical line colliding elastically with each other and the floor. Wojtkowski proved that for the system of two linear balls with a linear potential (with gravity), there is a periodic orbit which becomes linearly stable if m1

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.193-209
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• 2006

The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, much as the Reidemeister set does in Nielsen fixed point theory. In this paper, extending Cardona and Wong's work on relative Reidemeister numbers, we show that the Reidemeister orbit numbers can be used to calculate the relative essential orbit numbers. We also apply the relative Reidemeister orbit number to study periodic orbits of fibre preserving maps.

• Journal of the Korean Society for Precision Engineering
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• v.9 no.3
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• pp.157-164
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• 1992

This study concerns about the orbit prediction and orbit determination of Korean future communication satellite, called 'Moogunghwa", which will be motioned in the geo-stationary orbit. Perturbation effect on the satellite orbit due to nonspherical gravitation of the earth, gravitation of the sun and moon, radiation of sun, drag of the atmosphere was investigated. Cowell's method is used for orbit prediction. Orbit determination was performed by using Extended Kalman Filter which is suitable for real-time orbit determination. The result shows that the chacteristics of the satellite orbit has east-west and south-north drift. So the periodic control time and control value in the view of the periodic of error can be provided. The orbit determination demonstrated the effectiveness since the convergence performance on the positon and velocity error, and state error standard deviation is reasonable.able.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.692-697
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• 1992

This study concerns about the orbit prediction and orbit determination of Korean future communication satellite, called "Moogunghwa", which will be motioned in the geo-stationary orbit. Perturbation effect on the satellite orbit due to nonspherical geopotential term, lunar and solar gravity, drag force of the atmosphere and solar radiation pressure was investigated. Cowell's method is used for orbit prediction. Orbit determination was performed by using EKF which is suitable for real-time orbit determination. The result shows that the characteristics of the satellite orbit has drift. So the periodic control time and control value in the view of the periodic of error can be provided. The orbit determination demonstrated the effectiveness since the convergence performance on the position and velocity error , and state error standard deviation is reasonable.easonable.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1992.04a
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• pp.200-205
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• 1992

This study concerns about the orbit prediction and orbit determination of Korean future connumication satellite, called "Moogunghwa" , which will be motioned in the geo-stationary orbit. Perturbation effect on the satellite orbit due to nonspherical term, lunar and solar gravity, drag force of the atmospher, and solar radiation pressure was investigated. Cowell's method is used for orbit prediction. Orbit determination was performed by using Extended Kalman Filter which is suitable for real-time orbit determination. The result shows that the chacteristics of the satellite orbit has east-west and south-north drift. So the periodic control time and control value in the view of the periodic of error can be provided. The orbit determination demonstrated the effectiveness since the convergence performance on the positon and velocity error, and state error standard deviation is reasonable.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.67.5-67
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• 2001

A closed loop system with a linear plant and nonlinearity in the feedback connection is analyzed for its quasi-static orbital stability by a state-space approach. First a periodic orbit is assumed to exist in the loop which is determined by describing function method for the given nonlinearity. This is possible by selecting a proper nonlinearity and a rigorous justification of the describing function method.[1-3, 18, 20]. Then by introducing residual operator, a linear perturbed model can be formulated. Using various transformations like a modified eigenstructure decomposition, periodic-averaging, charge of variables and coordinate transformation, the stability of the periodic orbit, as a solution of harmonic balance, can be shown by investigating a simple scalar function and result of linear algebra. This is ...

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.871-878
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• 2010

In this paper, we show that if a homeomorphism has the pseudo-orbit-tracing-property and its nonwandering set is locally connected, then the points whose stable sets have nonempty interior are periodic points.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.341-347
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• 2012

The Reidemeister orbit set plays a crucial role in the Nielsen type theory of periodic orbits, much as the Reidemeister set does in Nielsen fixed point theory. Extending our work on Reidemeister orbit sets, we improve our theorem for formulae for Nielsen type essential orbit numbers.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.3 no.1
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• pp.1-6
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• 2003

The Delayed Feedback Control method (DFC) proposed by Pyragas applies an input based on the difference between the current state of the system, which is generating chaos orbits, and the $\tau$-time delayed state, and stabilizes the chaos orbit into a target. In DFC, the information about a position in the state space is unnecessary if the period of the unstable periodic orbit to stabilize is known. There exists the fault that DFC cannot stabilize the unstable periodic orbit when a linearlized system around the periodic point has an odd number property. There is the chaos control method using the prediction of the $\tau$-time future state (PDFC) proposed by Ushio et al. as the method to compensate this fault. Then, we propose a method such as improving the fault of the DFC. Namely, we combine DFC and PDFC with parameter W, which indicates the balance of both methods, not to lose each advantage. Therefore, we stabilize the state into the $\tau$ periodic orbit, and ask for the ranges of Wand gain K using Jury' method, and determine the quasi-optimum pair of (W, K) using a genetic algorithm. Finally, we apply the proposed method to a discrete-time chaotic system, and show the efficiency through some examples of numerical experiments.