Geodesic
Non-Hermitian Solutions of Algebraic Riccati Equations
Canadian journal of mathematics, Tome 49 (1997) no. 4, pp. 840-854

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-1997-043-4
Mots-clés : 15A99, 15A63, 93C60, Continuous algebraic Riccati equations, discrete algebraic Riccati equations, non-hermitian solutions.. 
Rodman, Leiba. Non-Hermitian Solutions of Algebraic Riccati Equations. Canadian journal of mathematics, Tome 49 (1997) no. 4, pp. 840-854. doi: 10.4153/CJM-1997-043-4
@article{10_4153_CJM_1997_043_4,
     author = {Rodman, Leiba},
     title = {Non-Hermitian {Solutions} of {Algebraic} {Riccati} {Equations}},
     journal = {Canadian journal of mathematics},
     pages = {840--854},
     year = {1997},
     volume = {49},
     number = {4},
     doi = {10.4153/CJM-1997-043-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1997-043-4/}
}
TY  - JOUR
AU  - Rodman, Leiba
TI  - Non-Hermitian Solutions of Algebraic Riccati Equations
JO  - Canadian journal of mathematics
PY  - 1997
SP  - 840
EP  - 854
VL  - 49
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1997-043-4/
DO  - 10.4153/CJM-1997-043-4
ID  - 10_4153_CJM_1997_043_4
ER  - 
%0 Journal Article
%A Rodman, Leiba
%T Non-Hermitian Solutions of Algebraic Riccati Equations
%J Canadian journal of mathematics
%D 1997
%P 840-854
%V 49
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1997-043-4/
%R 10.4153/CJM-1997-043-4
%F 10_4153_CJM_1997_043_4

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

Bittanti, S., Laub, A.J. and Willems, J.C. (eds.), The Riccati Equations, Springer Verlag, Berlin, 1991. Google Scholar

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

Faibusovich, L.E., Algebraic Riccati equation and symplectic algebra. Internat. J. Control 43(1986), 781– 792. Google Scholar

Gohberg, I., Lancaster, P. and Rodman, L., Matrices and Indefinite Scalar Products, OT8, Birkhäuser, 1983. Google Scholar

Gohberg, I., Invariant Subspaces of Matrices with Applications, John Wiley and Sons, New York, etc., 1986. Google Scholar

Lancaster, P. and Markus, A.S. and Ye, Q., Low rank perturbations of strongly definitizable transformations and matrix polynomials, Linear Algebra Appl. (1994), 3–29. Google Scholar

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

Lancaster, P. and Rodman, L., Existence and uniqueness theorems for the algebraic Riccati equations. Internat. J. Control 32(1980), 467–494. Google Scholar

Lancaster, P., Algebraic Riccati Equations, Oxford University Press, 1995. Google Scholar

Lancaster, P., Invariant neutral subspaces for symmetric and skewreal matrix pairs. Canad. J.Math. 46(1994), 602–618. Google Scholar

Lancaster, P., Minimal symmetric factorizations of symmetric real and complex rational matrix functions. Linear Algebra Appl. 220(1995), 249–282. Google Scholar

Mehrmann, V.L., The Autonomous Linear Quadratic Control Problem. Lecture Notes in Control and Information Sciences 163, Springer Verlag, Berlin, 1991. Google Scholar

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

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

Rodman, L., Maximal invariant neutral subspaces and an application to the algebraic Riccati equations. Manuscripta Math. 43(1983), 1–12. Google Scholar

Thompson, R.C., Pencils of complex and real symmetric and skew matrices. Linear Algebra Appl. 147(1991), 323–371. Google Scholar

Cité par Sources :