르장드르 웨이블릿을 이용한 선형 시불변 시스템의 효율적 수치 해석 방법

다국어 초록 (Multilingual Abstract)

In this paper Legendre wavelets are used to approximate the solutions of linear time-invariant system. The Legendre wavelet and its integral operational matrix are presented and an efficient algorithm to solve the Sylvester matrix equation is proposed. The algorithm is based on the decomposition of the Sylvester matrix equation and the preorder traversal algorithm. Using the special structure of the Legendre wavelet’s integral operational matrix, the full order Sylvester matrix equation can be solved in terms of the solutions of pure algebraic matrix equations, which reduce the computation time remarkably. Finally a numerical example is illustrated to demonstrate the validity of the proposed algorithm.

목차 (Table of Contents)

• Abstract
• Ⅰ. 서론
• Ⅱ. 르장드르 웨이블릿
• Ⅲ. 선형 시불변 시스템 해석 알고리즘
• Ⅳ. 수치 예
• Ⅴ. 결론
• REFERENCES

참고문헌 (Reference)

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4 H. R. Marzbana, "Solution of time-varying delay systems by hybrid functions" 64 : 597-607, 2004

5 B. M. Mohan, "Optimal control of nonlinear systems via orthogonal functions" 2011

6 J. Brewer, "Kronecker products and matrix calculus in system theory" 25 : 772-781, 1978

7 F. Ding, "Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle" 197 : 41-50, 2008

8 김범수, "Haar 웨이블릿을 이용한 선형시스템의 상태해석에 관한 연구" 제어·로봇·시스템학회 14 (14): 977-982, 2008

9 C. F. Chen, "Haar wavelet method for solving lumped and distributed-parameter systems" 144 : 87-94, 1997

10 B. S. Kim, "Combined preorder and postorder traversal algorithm for the analysis of singular systems by Haar wavelets" 2008