On the structure of balanced and other principal representations of SISO systems
- 1 February 1983
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 28 (2) , 228-231
- https://doi.org/10.1109/tac.1983.1103195
Abstract
A new matrix W co which can be considered as a cross-Gramian matrix which contains information about both controllability and observability is defined for single-input, single-output, linear systems. Using this matrix, the structural properties of linear systems are studied in the context of principal component analysis. The matrix W co can be used in obtaining balanced and other principal representations without computation of the controllability and the observability Gramians. The importance of this matrix in model-order reduction is highlighted.Keywords
This publication has 4 references indexed in Scilit:
- Model reduction via balanced state space representationsIEEE Transactions on Automatic Control, 1982
- Principal component analysis in linear systems: Controllability, observability, and model reductionIEEE Transactions on Automatic Control, 1981
- Synthesis of minimum roundoff noise fixed point digital filtersIEEE Transactions on Circuits and Systems, 1976
- Algorithm 432 [C2]: Solution of the matrix equation AX + XB = C [F4]Communications of the ACM, 1972