Explicit solutions of the discrete-time Lyapunov matrix equation and Kalman-Yakubovich equations
- 1 December 1981
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 26 (6), 1291-1294
- https://doi.org/10.1109/tac.1981.1102808
Abstract
A general solution for the nonsquare nonsymmetric Lyapunov matrix equation in a canonical form is presented. The solution is shown to be a Toeplitz matrix which may be calculated using the backwards Levinson algorithm This solution is then applied to the Kalman-Yakubovich equations to derive a method for generating strictly positive-real functions via the positive-real lemma. This latter result has an application in system identification.Keywords
This publication has 23 references indexed in Scilit:
- Analysis of the Lyapunov equation using generalized positive real matricesIEEE Transactions on Automatic Control, 1980
- Elimination of the real positivity condition in the design of parallel MRASIEEE Transactions on Automatic Control, 1978
- Inverses of Toeplitz Operators, Innovations, and Orthogonal PolynomialsSIAM Review, 1978
- Solution of the optimal constant output feedback problem by conjugate gradientsIEEE Transactions on Automatic Control, 1974
- A view of three decades of linear filtering theoryIEEE Transactions on Information Theory, 1974
- Algorithms for Triangular Decomposition of Block Hankel and Toeplitz Matrices with Application to Factoring Positive Matrix PolynomialsMathematics of Computation, 1973
- Algebraic solution of matrix linear equations in control theoryProceedings of the Institution of Electrical Engineers, 1969
- Matrix calculations for Liapunov quadratic formsJournal of Differential Equations, 1966
- The Theory of MatricesPublished by Springer Nature ,1933
- ber die Anzahl der Wurzeln einer algebraischen Gleichung in einem KreiseMathematische Zeitschrift, 1922