Spectral and Inner-Outer Factorizations of Rational Matrices
- 1 January 1989
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Matrix Analysis and Applications
- Vol. 10 (1) , 1-17
- https://doi.org/10.1137/0610001
Abstract
Spectral factorization and inner-outer factorization are basic techniques in treating many problems in electrical engineering. In this paper, the roblems of doing spectral and inner-outer factorizations via state-space methods are studied when the matrix to be factored is real-rational and surjective on the extended maginary axis. It is shown that our factorization problems can be reduced to solving a certain constrained Riccati equation, and that by examining some invariant ubspace of the associated Hamiltonian matrix there exists a unique solution to this equation. Finally, a state-space procedure to perform the factorization is proposed.Keywords
This publication has 12 references indexed in Scilit:
- A Course in H∞ Control TheoryPublished by Springer Nature ,1987
- A Hamiltonian $QR$ AlgorithmSIAM Journal on Scientific and Statistical Computing, 1986
- Monotonicity of maximal solutions of algebraic Riccati equationsSystems & Control Letters, 1985
- Linear Multivariable ControlPublished by Springer Nature ,1985
- H∞-optimal feedback controllers for linear multivariable systemsIEEE Transactions on Automatic Control, 1984
- Feedback, minimax sensitivity, and optimal robustnessIEEE Transactions on Automatic Control, 1983
- Factorizations of Transfer FunctionsSIAM Journal on Control and Optimization, 1980
- Ill-Conditioned Eigensystems and the Computation of the Jordan Canonical FormSIAM Review, 1976
- An algebraic solution to the spectral factorization problemIEEE Transactions on Automatic Control, 1967
- Matrix Quadratic SolutionsSIAM Journal on Applied Mathematics, 1966