Similarity transformations involving the schwarz and companion matrices
- 1 April 1969
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 14 (2), 205-206
- https://doi.org/10.1109/tac.1969.1099153
Abstract
Krylov's algorithm is used to unify and extend recent work on relating a matrix to its companion form and the companion matrix to the Schwarz form. A general solution to the "inverse problem of stability" is presented and illustrated.Keywords
This publication has 8 references indexed in Scilit:
- A simplified proof of a transformation matrix relating to the companion matrix and Schwarz matrixIEEE Transactions on Automatic Control, 1968
- A general proof of the Pnmatrix and its inverseIEEE Transactions on Automatic Control, 1967
- The companion matrix and Liapunov functions for linear multivariable time-invariant systemsJournal of the Franklin Institute, 1967
- Solution of the Lyapunov matrix equation with a diagonal input matrix, obtained without matrix inversionElectronics Letters, 1967
- A matrix for evaluating Schwarz's formIEEE Transactions on Automatic Control, 1966
- Comment on "A new proof of the Routh-Hurwitz stability criterion by the second method of Lyapunov with applications to optimum transfer functions"IEEE Transactions on Automatic Control, 1964
- Matrix functions and applications: Part V — Similarity reductions by rational or orthogonal matricesIEEE Spectrum, 1964
- Optimal Bang-Bang Control With Quadratic Performance IndexJournal of Basic Engineering, 1964