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On the algebraic Riccati equation

Published online by Cambridge University Press:  17 April 2009

Harald K. Wimmer
Harald K. Wimmer
Affiliation:
Mathematisches Institut der Universität, Würzburg, Germany Mathematisches Institut, Technische Universität Graz, Graz, Austria.
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Abstract

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In this note the matrix equation A + WB + BTW + WCW = 0 is considered. A monotoneity result and an inertia theorem on the location of the eigenvalues of W and B + CW are proved.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 14 , Issue 3 , June 1976 , pp. 457 - 461
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Athans, Michael, Falb, Peter L., Optimal control. An introduction to the theory and its applications (McGraw-Hill, New York, St. Louis, San Francisco, Toronto, London, Sydney, 1966).Google Scholar
[2]Brockett, Roger W., Finite dimensional linear systems (John Wiley & Sons, New York, London, Sydney, Toronto, 1970).Google Scholar
[3]Chen, Chi-Tsong, “A generalization of the inertia theorem”, SIAM J. Appl. Math. 25 (1973), 158–161.Google Scholar
[4]Coppel, W.A., “Matrix quadratic equations”, Bull. Austral. Math. Soc. 10 (1974), 377–401.Google Scholar
[5]Hautus, M.L.J., “Controllability and observability conditions of linear autonomous systems”, Proc. K. Nederl. Akad. Wetensch. Amsterdam Ser. A 72 (1969), 443–448.Google Scholar
[6]Ostrowski, Alexander and Schneider, Hans, “Some theorems on the inertia of general matrices”, J. Math. Anal. Appl. 4 (1962), 72–84.CrossRefGoogle Scholar
[7]Willems, Jan C., “Least squares stationary optimal control and the algebraic Riccati equation”, IEEE Trans. Automatic Control AC-16 (1971), 621–634Google Scholar
[8]Wimmer, Harald K., “Inertia theorems for matrices, controllability, and linear vibrations”, Linear Algebra and Appl. 8 (1974), 337–343.CrossRefGoogle Scholar