Shift Walsh matrix and delay-differential equations
- 1 December 1978
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 23 (6) , 1023-1028
- https://doi.org/10.1109/tac.1978.1101888
Abstract
Shift Walsh matrix is first introduced. The shift Walsh matrix is formed from the Walsh matrix by shifting the columns of the Walsh matrix to the right, dropping the last columns and assigning first columns of the new matrix as zero elements. Delay Walsh functions can be expanded in terms of Walsh functions using shift Walsh matrix. Therefore, linear delay-differential equations can he analyzed by Walsh series approximation. The method is most useful for time-varying systems.Keywords
This publication has 10 references indexed in Scilit:
- Analytical solutions of delay‐differential equations via a time‐partition methodJournal of the Chinese Institute of Engineers, 1987
- Analysis and optimal control of time-varying linear systems via Walsh functionsInternational Journal of Control, 1978
- Design of piecewise constant gains for optimal control via Walsh functionsIEEE Transactions on Automatic Control, 1975
- A state-space approach to Walsh series solution of linear systemsInternational Journal of Systems Science, 1975
- Walsh series analysis in optimal controlInternational Journal of Control, 1975
- Explicit solution of a class of delay-differential equationsInternational Journal of Control, 1975
- Time-domain synthesis via Walsh functionsProceedings of the Institution of Electrical Engineers, 1975
- Orthogonal Transforms for Digital Signal ProcessingPublished by Springer Nature ,1975
- Solution of differential and integral equations with Walsh functionsIEEE Transactions on Circuit Theory, 1973
- A Remarkable Series of Orthogonal Functions (I)Proceedings of the London Mathematical Society, 1932