• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.933-942
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• 2014

We give a representation of the component of solutions with characteristic multiplier 1 in a periodic linear inhomogeneous continuous system. It follows from this representation that asymptotic behaviors of the component of solutions to the system and to its associated homogeneous system are quite different, though they are similar in the case where the characteristic multiplier is not 1. Moreover, the representation is applicable to linear discrete systems with constant coefficients.

• 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

• Journal of the Korean Society for Precision Engineering
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• v.17 no.12
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• pp.121-128
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• 2000

The scope of this paper is focused to the systems which have the time period and they should be necessarily studied in the sense of stability and design method of controller to stabilize the orignal unstable systems. In general, the time periodic systems or the systems having same motions during certain time interval are easily found in rotating motion device, i.e., satellite or helicopter and widely used in factory automation systems. The characteristics of the selected dynamic systems are analyzed with the new stability concept and stabilization control method based on Lyapunov direct method. The new method from Lyapunov stability criteria which satisfies the energy convergence is studied with linear algebraic method. And the numerical procedures are developed with computational programming method to apply to the practical linear periodic systems. The results from this paper demonstrate the usefulness in analysis of the asymptotic stability and stabilization of the unstable linear periodic system by using the developed simulation procedures.

• 제어로봇시스템학회:학술대회논문집
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• 1990.10b
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• pp.1139-1144
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• 1990

In this paper, we consider linear periodic discrete-time control systems under periodic compensation. Such a closed-loop system generally represents a periodic time-varying system. We examine the problem of finding a compensator such that the closed-loop system is realized as LTI model (if possible) with the closed-loop stability being satisfied. We present a necessary and sufficient condition for solving such problem and also give the characterization of realizable LTI models.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1770-1773
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• 1997

In this paper, a linear discrete time system subject to the input saturatioin is shown to be exponentially stabilizable on any compact subset of the constrained asymptotically stabilizable set by a linear periodic variable structure controller. We also establish tat any neutrally stable system subject to the input saturation can be globally asymptotically stabilizable via linear feedback.

• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.83-87
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• 1999

The purpose of this study is to provide the new method for selection of a close to optimal scalar control of linear time-periodic system. The case of scalar control is considered, the gain matrix being assumed to be at worst periodic with the system period T. The form of gain matrix may have various kinds but must have same period, for example, one of each element being represented by Fourier series. As the optimal gain matrix I consider the matrix ensuring the minimum value of the larger real part of the Poincare exponents of the system. Finally we present a pole placement algorithm to make the given system be stable. It is possible to determine the stability of the given periodic system without get the analytic solution. The application of the method does not require the construction of the Floquet solution. At present state of determination of the gain matrix for this case will be done only by systematic numerical search procedures.

• Kyungpook Mathematical Journal
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• v.60 no.2
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• pp.401-413
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• 2020

In this article we consider the following system of piecewise linear difference equations: x_n+1 = |x_n| - y_n - 1 and y_n+1 = x_n + |y_n| - 1. We show that when the initial condition is an element of the closed second or fourth quadrant the solution to the system is either a prime period-3 solution or one of two prime period-4 solutions.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.4 no.5
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• pp.963-969
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• 2000

In this paper, we define two input-output gains of linear periodic time-varying systems. One is the ratio of output with worst-case l2-norm over all inputs with unit 12-norm. It denotes G($\iota_2,\iota_2$.The other is the ratio of output with worst-case RMS value over all inputs with unit RMS value. It denotes G(RMS, RMS) .It is fact that these two gains are equivalent for linear time-invariant system. In this paper, we prove these two gains are also equivalent for linear periodic time-varying system. In addition, the relationship between two method of obtaining the generalized frequency responses for linear periodic time-varying system is derived. Finally, we apply the defined input-output gains to M-channel filter-bank which is multi-rate signal Processing system, used to speech coding. In the filter-bank, generally, aliasing distortion, magnitude distortion, and phase distortion are present. It is shown that these are kept small if the filter-bank is designed by a method that optimizes the gain G($\iota_2,\iota_2$ of an error system.

• 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 ...

• Bulletin of the Korean Mathematical Society
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• v.22 no.2
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• pp.95-98
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• 1985

In [1], E.B. Lee and L. Markus described a sufficient condition for which the domain of null-controllability of a linear autonomous system is all of R$^{n}$ . The purpose of this note is to extend the result to a certain linear nonautonomous system. Thus we consider a linear control system dx/dt = A(t)x+B(t)u in the Eculidean n-space R$^{n}$ where A(t) and B(t) are n*n and n*m matrices, respectively, which are continuous on 0.leq.t<.inf. and A(t) is a periodic matrix of period .omega.. Admissible controls are bounded measurable functions defined on some finite subintervals of [0, .inf.) having values in a certain convex set .ohm. in R$^{m}$ with the origin in its interior. And we present a sufficient condition for which the domain of null-controllability is all of R$^{n}$ .