A state-space approach to indefinite spectral factorization

SIAM Journal on Matrix Analysis and Applications

Volumn 21, Issue 3, 2000, Pages 743-767

  Clements, D J ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Rational matrices; Spectral factorization

Indexed keywords

EID: 0034342184     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479897324469     Document Type: Article

References (26)

1. H. BART, I. GOHBERG, AND M. A. KAASHOEK, Minimal Factorization of Matrix and Operator Functions, Oper. Theory Adv. Appl. 1, Birkhäuser, Basel, 1979.
2. H. BART, I. GOHBERG, M. A. KAASHOEK, AND P. VAN DOOREN, Factorization of transfer functions, SIAM J. Control Optim., 18 (1980), pp. 675-696.
3. P. BERNHARD, On singular implicit linear dynamical systems, SIAM J. Control Optim., 20 (1982), pp. 612-633.
4. D. J. CLEMENTS, A State-Space Approach to J-Spectral Factorization, Internal Report: UNSW, University of New South Wales, Sydney, Australia, 1993.
5. D. J. CLEMENTS AND K. GLOVER, Spectral factorization via Hermitian pencils, Linear Algebra Appl., 122-124 (1989), pp. 797-846.
6. W. A. COPPEL, Linear Systems, Notes in Pure Mathematics 6, Australian National University, Canberra, 1972.
7. D. Z. DOKOVIC, Factorization of Hermitian matrix polynomials with constant signature, Linear Algebra Appl., 194 (1993), pp. 85-90.
8. ∞ control problems, IEEE Trans. Automat. Control, 32 (1987), pp. 831-847.
9. I. GOHBERG AND M. A. KAASHOEK, EDS., Constructive Methods of Wiener-Hopf Factorization, Oper. Theory Adv. Appl. 21, Birkhäuser, Basel, 1986.
10. I. GOHBERG, P. LANCASTER, AND L. RODMAN, Factorization of selfadjoint matrix polynomials with constant signature, Linear and Multilinear Algebra, 11 (1982), pp. 209-214.
11. I. GOHBERG, P. LANCASTER, AND L. RODMAN, Matrix Polynomials, Computer Science and Applied Mathematics, Academic Press, New York, 1982.
12. ∞ controller synthesis by J-lossless coprime factorization, SIAM J. Control Optim., 30 (1992), pp. 522-547.
13. ∞ control, SIAM J. Control Optim., 28 (1990), pp. 1350-1371.
14. J. GRIMM, Realization and canonicity for implicit systems, SIAM J. Control Optim., 26 (1988), pp. 1331-1347.
15. V. K. JACUBOVIC, Factorization of symmetric matrix polynomials, Soviet Mathematics Doklady, 11 (1970), pp. 1261-1264.
16. B. D. JJUBACEVSKII, A representation of a symmetric polynomial matrix, Vestnik Leningrad Univ. Math., 5 (1978), pp. 245-249.
17. M. KUIJPER AND J. SCHUMACHER, Minimality of descriptor representations under external equivalence, Automatica, 27 (1991), pp. 985-995.
18. ∞-optimization - tutorial paper, Automatica, 29 (1993), pp. 255-273.
19. H. KWAKERNAAK AND M. SEBEK, Polynomial J-spectral factorization, IEEE Trans. Automat. Control, 39 (1994), pp. 315-328.
20. P. LANCASTER AND L. HODMAN, Existence and uniqueness theorems for the algebraic Riccati equation, Internat. J. Control, 32 (1980), pp. 285-309.
21. A. C. M. RAN AND L. RODMAN, On symmetric factorizations of rational matrix functions, Linear and Multilinear Algebra, 29 (1991), pp. 243-261.
22. M. SEBEK, An Algorithm for Spectral Factorization of Polynomial Matrices with Any Signature, Technical Report 912, University of Twente, The Netherlands, 1990.
23. M. SEBEK AND H. KWAKERNAAK, J-spectral factorization, in Proceedings of the 30th IEEE Decision and Control Conference, Brighton, UK, 1991, pp. 1278-1283.
24. R. C. THOMPSON, The characteristic polynomial of a principal subpencil of an Hermitian matrix pencil, Linear Algebra Appl., 14 (1976), pp. 135-177.
25. ∞ control in a behavioral context, in Proceedings of the 33rd IEEE Decision and Control Conference, Lake Buena Vista, FL, 1994, pp. 3695-3700.
26. D. C. YOULA, On the factorization of rational matrices, IRE Transactions on Information Theory, IT-7 (1961), pp. 172-189.