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Non-Hermitian Solutions of Algebraic Riccati Equations

Published online by Cambridge University Press:  20 November 2018

Leiba Rodman
Leiba Rodman*
Affiliation:
Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187-8795, U.S.A. e-mail: lxrodm@math.wm.edu
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Abstract

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Non-hermitian solutions of algebraic matrix Riccati equations (of the continuous and discrete types) are studied. Existence is proved of non-hermitian solutions with given upper bounds of the ranks of the skew-hermitian parts, under the sign controllability hypothesis.

Keywords

15A9915A6393C60Continuous algebraic Riccati equationsdiscrete algebraic Riccati equationsnon-hermitian solutions..
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 4 , 01 August 1997 , pp. 840 - 854
Copyright
Copyright © Canadian Mathematical Society 1997

References

[AI] Ya.|Azizov, T. and Iokhvidov, I.S.. Linear Operators in Spaces with Indefinite Metric, J. Wiley & Sons, Chichester etc., 1989. translated from Russian.Google Scholar
[BLW] Bittanti, S., Laub, A.J. and Willems, J.C. (eds.), The Riccati Equations, Springer Verlag, Berlin, 1991.Google Scholar
[DPWZ] Djokovi, D.Z.č, Potera, J., Winternitz, P. and Zassenhaus, H., Normal forms of elements of classical real and complex Lie and Jordan algebras. J. Math. Phys. 24(1983), 1363–1374.Google Scholar
[F] Faibusovich, L.E., Algebraic Riccati equation and symplectic algebra. Internat. J. Control 43(1986), 781– 792.Google Scholar
[GLR1] Gohberg, I., Lancaster, P. and Rodman, L., Matrices and Indefinite Scalar Products, OT8, Birkhäuser, 1983.Google Scholar
[GLR2] Gohberg, I., Invariant Subspaces of Matrices with Applications, John Wiley and Sons, New York, etc., 1986.Google Scholar
[LMY] Lancaster, P. and Markus, A.S. and Ye, Q., Low rank perturbations of strongly definitizable transformations and matrix polynomials, Linear Algebra Appl. 197/198(1994), 3–29.Google Scholar
[LRR] Lancaster, P., Ran, A.C.M. and Rodman, L., Hermitian solutions of the discrete algebraic Riccati equations. Internat. J. Control 44(1986), 777–802.Google Scholar
[LR1] Lancaster, P. and Rodman, L., Existence and uniqueness theorems for the algebraic Riccati equations. Internat. J. Control 32(1980), 467–494.Google Scholar
[LR2] Lancaster, P., Algebraic Riccati Equations, Oxford University Press, 1995.Google Scholar
[LR3] Lancaster, P., Invariant neutral subspaces for symmetric and skewreal matrix pairs. Canad. J.Math. 46(1994), 602–618.Google Scholar
[LR4] Lancaster, P., Minimal symmetric factorizations of symmetric real and complex rational matrix functions. Linear Algebra Appl. 220(1995), 249–282.Google Scholar
[M] Mehrmann, V.L., The Autonomous Linear Quadratic Control Problem. Lecture Notes in Control and Information Sciences 163, Springer Verlag, Berlin, 1991.Google Scholar
[PLS] Pappas, T., Laub, A.J. and Sandell, N.R., On the numerical solutions of the discrete-time algebraic Riccati equations. IEEE Trans. Automat. Control 25(1980), 631–641.Google Scholar
[RR] Ran, A.C.M. and Rodman, L., Stability of invariant Lagrangian subspaces I. Operator Theory: Advances and Applications (ed. Gohberg, I.), 32(1988), 181–218.Google Scholar
[R] Rodman, L., Maximal invariant neutral subspaces and an application to the algebraic Riccati equations. Manuscripta Math. 43(1983), 1–12.Google Scholar
[T] Thompson, R.C., Pencils of complex and real symmetric and skew matrices. Linear Algebra Appl. 147(1991), 323–371.Google Scholar