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All issues Volume 4 (1999) ESAIM: COCV, 4 (1999) 609-630 References
Free Access
Issue
ESAIM: COCV
Volume 4, 1999
Page(s) 609 - 630
DOI https://doi.org/10.1051/cocv:1999125
Published online 15 August 2002
  1. G. Ammar and C. Martin, The geometry of matrix eigenvalue methods. Acta Appl. Math. 5 (1986) 239-279. [CrossRef] [MathSciNet] [Google Scholar]
  2. F.A. Badawi and A. Lindquist, A Hamiltonian approach to the factorization of the matrix Riccati equation. Math. Programming Stud. 18 (1982) 27-38. [Google Scholar]
  3. C.I. Byrnes, A. Lindquist, S.V. Gusev and S. Matee, A complete parametrization of all positive rational extensions of a covariance sequence. IEEE Trans. Automat. Control AC-40 (1995) 1841-1857. [Google Scholar]
  4. C.I. Byrnes and A. Lindquist, On the partial stochastic realization problem. IEEE Trans. Automat. Control AC-42 (1997) 1049-1070. [Google Scholar]
  5. C.I. Byrnes, A. Lindquist and T. McGregor, Predictability and unpredictability in Kalman filtering. IEEE Trans. Automat. Control 36 (1991) 563-579. [CrossRef] [MathSciNet] [Google Scholar]
  6. C.I. Byrnes, A. Lindquist and Y. Zhou, Stable, unstable and center manifolds for fast filtering algorithms. Modeling, Estimation and Control of Systems with Uncertainty, G.B. Di Masi, A. Gombani and A. Kurzhanski, Eds., Birkhäuser Boston Inc. (1991). [Google Scholar]
  7. , On the nonlinear dynamics of fast filtering algorithms. SIAM J. Control Optim. 32 (1994) 744-789. [CrossRef] [MathSciNet] [Google Scholar]
  8. J.W.S. Cassels, An Introduction to Diophantine Approximation, Cambridge University Press, Cambridge (1956). [Google Scholar]
  9. H.J. Landau, C.I. Byrnes and A. Lindquist, On the well-posedness of the rational covariance extension problem, Tech. Report TRITA/MAT-96-OS5, Department of Mathematics, KTH, Royal Institute of Technology, Stockholm, Sweden (1996). [Google Scholar]
  10. S.V. Gusev, C.I. Byrnes and A. Lindquist, A convex optimization approach to the rational covariance extension problem, Tech. Report TRITA/MAT-97-OS9, Department of Mathematics, KTH, Royal Institute of Technology, Stockholm, Sweden (1997). [Google Scholar]
  11. P. Faurre, M. Clerget and F. Germain, Opérateurs Rationnels Positifs, Dunod (1979). [Google Scholar]
  12. G.H. Hardy and J.E. Littlewood, Some problems of Diophantine approximation. Acta Math. 37 (1914) 155-239. [CrossRef] [MathSciNet] [Google Scholar]
  13. G.H. Hardy and E.M. Wright, An Introduction to the Theory of Numbers, Oxford at the Clarendon Press (1954). [Google Scholar]
  14. R. Hermann and C. Martin, Lie and Morse theory for periodic orbits of vector fields and matrix Riccati equations, I: General Lie-theoretic methods. Math. Systems Theory 15 (1982) 277-284. [CrossRef] [Google Scholar]
  15. , Lie and Morse theory for periodic orbits of vector fields and matrix Riccati equations. II. Math. Systems Theory 16 (1983) 297-306. [CrossRef] [MathSciNet] [Google Scholar]
  16. J.F. Koksma, Diophantische Approximationen, Chelsea Publishing Company, New York (1936). [Google Scholar]
  17. A.J. Laub and K. Meyer, Canonical forms for symplectic and Hamiltonian matrices. Celestial Mech. 9 (1974) 213-238. [Google Scholar]
  18. A. Lindquist, A new algorithm for optimal filtering of discrete-time stationary processes. SIAM J. Control 12 (1974) 736-746. [CrossRef] [MathSciNet] [Google Scholar]
  19. , Some reduced-order non-Riccati equations for linear least-squares estimation: the stationary, single-output case. Int. J. Control 24 (1976) 821-842. [CrossRef] [Google Scholar]
  20. C. Martin, Grassmannian manifolds, Riccati equations, and feedback invariants of linear systems, Geometrical Methods for the Theory of Linear Systems, C.I. Byrnes and C. Martin, Eds., Reidel Publishing Company (1980) 195-211. [Google Scholar]
  21. I. Niven, Diophantine Approximations, Interscience Publishers, New York, London (1956). [Google Scholar]
  22. I.R. Shafarevitch, Basic Algebraic Geometry, Springer-Verlag, Heidelberg (1974). [Google Scholar]
  23. M. Shayman, Phase portrait of the matrix Riccati equations. SIAM J. Control Optim. 24 (1986) 1-65. [CrossRef] [MathSciNet] [Google Scholar]
  24. Y. Zhou, Monotonicity and finite escape time of solutions of the discrete-time riccati equation, to appear in proceedings of European Control Conference, Karlsruhe (1999). [Google Scholar]

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