• The Mathematical Education
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• v.27 no.1
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• pp.29-35
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• 1988

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.225-228
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• 1992

The purpose of this project is the presentation of new method for selection of a scalar control of linear time-periodic system. The approach has been proposed by Radziszewski and Zaleski [4] and utilizes the quadratic form of Lyapunov function. The system under consideration is assigned either in closed-loop state or in modal variables as in Calico, Wiesel [1]. The case of scalar control is considered, the gain matrix being assumed to be at worst periodic with the system period T, each element being represented by a Fourier series. As the optimal gain matrix we consider the matrix ensuring the minimum value of the larger real part of the two Poincare exponents of the system. The method, based on two-step optimization procedure, allows to find the approximate optimal gain matrix. At present state of art determination of the gain matrix for this case has been done by systematic numerical search procedure, at each step of which the Floquet solution must be found.

• 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.

• International Journal of Control, Automation, and Systems
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• v.5 no.6
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• pp.712-717
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• 2007

This paper is concerned with the problem of state feedback control of continuous-time nonlinear Markovian jump systems, which are represented by Takagi-Sugeno fuzzy models. A new method for designing state feedback stabilizing controllers is presented in terms of solvability of a set of linear matrix inequalities (LMIs), and it is shown that the new design method provides better or at least the same results of the existing method in the literature. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1271-1286
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• 2015

An operator T on a complex Hilbert space H is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for H. In this paper, we study skew symmetric operators with eigenvalues. First, we provide an upper-triangular operator matrix representation for skew symmetric operators with nonzero eigenvalues. On the other hand, we give a description of certain skew symmetric triangular operators, which is based on the geometric relationship between eigenvectors.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2013-2027
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• 2017

We compute explicitly the matrices represented by Toeplitz operators on the Hardy space over the unit circle with respect to a special orthonormal basis constructed by author in terms of their symbols. And we also find a necessary condition for the matrix generated by the product of two Toeplitz operators with respect to the basis to be a Toeplitz matrix by a direct calculation and we finally solve commuting problems of two Toeplitz operators in terms of symbols. This is a generalization of the classical results obtained regarding to the orthonormal basis consisting of the monomials.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.867-880
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• 1996

Numerical approximations to the linear elasticity are traditionally based on the finite element method. In this paper we propose a new formulation based on the cubic spline collocation method for linear elastic problem on the unit square. We present several numerical results for the eigenvalues of the matrix represented by cubic collocation method and preconditioner matrix which is preconditioned by FEM and FDM. Finally we present the numerical solution for some example equation.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1421-1441
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• 2017

We compute explicitly the matrix represented by the Toeplitz operator on the Hardy space over a smoothly finitely connected bounded domain in the plane with respect to special orthonormal bases consisting of the classical kernel functions for the space of square integrable functions and for the Hardy space. The Fourier coefficients of the symbol of the Toeplitz operator are obtained from zeroth row vectors and zeroth column vectors of the matrix. And we also find some condition for the product of two Toeplitz operators to be a Toeplitz operator in terms of matrices.

• 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).

• Proceedings of the KIEE Conference
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• 2005.10b
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• pp.523-525
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• 2005

This paper deals with a linear matrix inequality (LMI) approach to the design of a static output feedback controller that simultaneously stabilizes a finite collection of linear time-invariant plants. Simultaneous stabilization by static ouput feedback is represented in terms of LMIs with a rank condition. An iterative penalty method is proposed to solve the rank-constrained LMI problem. Numerical experiments show the effectiveness of the proposed algorithm.