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Maximal invariant neutral subspaces and an application to the algebraic Riccati equation

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Abstract

For a matrix A which is selfadjoint with respect to an indefinite scalar product, a description of maximal A-invariant neutral subspaces is provided. This description is motivated by the characterization of hermitian solutions of an algebraic Riccati equation.

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References

  1. BOGNAR,J.: Indefinite inner product spaces. New York-Heidelberg-Berlin, Springer 1974.

    Google Scholar 

  2. COPPEL, W.A.: Matrix quadratic equations. Bull. Austral. Math. Soc.10, 377–401 (1974).

    Google Scholar 

  3. GOHBERG, I., LANCASTER, P., & RODMAN, L.: Spectral analysis of selfadjoint matrix polynomials. Res. Paper No. 419, Dept. of Mathematics and Statistics, University of Calgary, Canada (1979).

    Google Scholar 

  4. GOHBERG, I., LANCASTER, P., & RODMAN, L.: Perturbations of H-selfadjoint matrices with applications to differential equations. To appear in Integral Equations and Operator Theory.

  5. GOHBERG, I., LANCASTER, P., & RODMAN, L.: Matrix polynomials. To appear in Academic Press.

  6. HUA, L.K.: On the theory of automorphic functions of a matrix variable, II. The classification of hypercircles under the symplectic group. Amer. J. Math.66, 531–563 (1944).

    Google Scholar 

  7. LANCASTER, P., RODMAN, L.: Existence and uniqueness theorems for the algebraic Riccati equation. Int. J. Control32, 285–309 (1980).

    Google Scholar 

  8. MAL'LEV, A.I.: Foundations of Linear Algebra. San Francisco-London, W.H. Freeman 1963.

    Google Scholar 

  9. MARTENSSON, K.: On the matrix Riccati equation. Information Sciences3, 17–49 (1971).

    Google Scholar 

  10. POTTER, J.E.: Matrix quadratic solutions. J. SIAM Appl. Math.14, 496–501 (1966).

    Google Scholar 

  11. SHAYMAN, M.A.: Classification theorems for the algebraic Riccati equation: a synthesis. International Symposium on Mathematical Theory of Networks and Systems4, 257–261 (1981).

    Google Scholar 

  12. SHAYMAN, M.A.: Geometry of the algebraic Riccati equation. In preparation.

  13. WILLEMS, J.C.: Least Squares Stationary Optimal Control and the Algebraic Riccati Equation. IEEE Trans. on Aut. Cont.AC-16, 621–634 (1971).

    Google Scholar 

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Rodman, L. Maximal invariant neutral subspaces and an application to the algebraic Riccati equation. Manuscripta Math 43, 1–12 (1983). https://doi.org/10.1007/BF01169094

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  • DOI: https://doi.org/10.1007/BF01169094

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