• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.6
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• pp.606-613
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• 1988

This paper presents an unified method of obtaining the inverse of a matrix whose elements are a linear combination of piecewise constant functions. We show that the inverse of such a matrix can be obtained by solving a set of linear algebraic equations.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.43 no.4
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• pp.648-657
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• 1994

This paper presents a solution of the H$\infty$ control problem for a linear singularly perturbed system. A sufficient condition for a linear singularly perturbed system to achieve the prescribed disturbance attenuation level is obtained. Based upon this sufficient condition, an H$\infty$ controller design method which involves the solutions of two generalized algebraic Riccati equations(GRE) is developed.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.8
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• pp.1434-1439
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• 2008

Numerical methods for solving the state feedback control problem of linear time invariant system are presented in this paper. The methods are based on Haar wavelet approximation. The properties of Haar wavelet are first presented. The operational matrix of integration and its inverse matrix are then utilized to reduce the state feedback control problem to the solution of algebraic matrix equations. The proposed methods reduce the computation time remarkably. Finally a numerical example is illustrated to demonstrate the validity and applicability of the proposed methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.2
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• pp.67-80
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• 1998

In this paper the linear algebraic system obtained from a singular integral equation with variable coeffcients by a quadrature-collocation method is considered. We study this underdetermined system by means of the Moore Penrose generalized inverse. Convergence in compact subsets of [-1, 1] can be shown under some assumptions on the coeffcients of the equation.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.52 no.4
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• pp.198-204
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• 2003

In this paper, we presented a new algebraic iterative algorithm for the optimal control of the nonlinear systems. The algorithm is based on two steps. The first step transforms nonlinear optimal control problem into a sequence of linear optimal control problem using the quasilinearization method. In the second step, TPBCP(two point boundary condition problem) is solved by algebraic equations instead of differential equations using the new integral operational matrix of BPF(block pulse functions). The proposed algorithm is simple and efficient in computation for the optimal control of nonlinear systems and is less error value than that by the conventional matrix. In computer simulation, the algorithm was verified through the optimal control design of synchronous machine connected to an infinite bus.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.561-577
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• 2002

In this paper, a two-dimensional finite volume unstructured mesh method (FVUM) based on a triangular background interpolation mesh is developed for analysing the evolution of the saltwater intrusion into single and multiple coastal aquifer systems. The model formulation consists of a ground-water flow equation and a salt transport equation. These coupled and non-linear partial differential equations are transformed by FVUM into a system of differential/algebraic equations, which is solved using backward differentiation formulas of order one through five. Simulation results are compared with previously published solutions where good agreement is observed.

• Journal of Electrical Engineering and Technology
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• v.7 no.1
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• pp.124-131
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• 2012

This paper deals with robust stability of linear time-invariant (LTI) systems with unstructured uncertainties. A new relation between uncertainties and system poles perturbed by the uncertainties is derived from a graphical analysis. A stability criterion for LTI systems with uncertainties is proposed based on this result. The migration range of the poles in the proposed criterion is represented as the bound of uncertainties, the condition number of a system matrix, and the disc containing the poles of a given nominal system. Unlike the existing methods depending on the solutions of algebraic matrix equations, the proposed criterion provides a simpler way which does not involves algebraic matrix equations, and a more flexible root clustering approach by means of adjusting the center and the radius of the disc as well as the condition number.

• Computational Structural Engineering
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• v.10 no.2
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• pp.265-272
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• 1997

The purpose of this paper is to develop Neural Network models for Approximate Structural Analysis (NNASA). As an initial stage, the paper classifies the characteristics and the active role of neural networks in the numerical analysis by comparing neural networks with conventional numerical analysis algorithms. The paper proposed two methods of finding solutions of linear algebraic equations by a modified neural network algorithm, and presents that multilayer feedforward networks are a class of universal approximators by comparing the neural network with regression and interpolation techniques.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.49 no.3
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• pp.111-116
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• 2000

In this paper, we presented a new algebraic iterative algorithm for the optimal control of the nonlinear systems. The algorithm is based on tow steps. The first step transforms optimal control problem into a sequence of linear optimal control problem using the quasilinearization method. In the second step, TPB(two point boundary condition problem) is solved by algebraic equations instead of differential equations using BPF(block pulse functions). The proposed algorithm is simple and efficient in computation for the optimal control of nonlinear systems. In computer simulation, the algorithm was verified through the optimal control design of Van del pole system and Volterra Predatory-prey system.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.3
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• pp.263-269
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• 1999

In this paper, an unifying design algorithm is presented for efficient digital implementation of continuous PID controller using general discrete orthogonal functions. The proposed algorithm is an algebraic method to determine controller parameters, which can unify controller design procedures divided into three ways. A set of linear equations for the controller design are derived from simple algebraic transformation based on general discrete orthogonal functions. By solving these equations, all of the controller parameters can be determined directly and simultaneously, which thus makes the design procedure systematic and straightforward. It does not involve any trial and error procedure, hence the difficulty of conventional approach can be avoided. The simulation results and discussions are given to demonstrate the efficiency of the proposed method.