Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-25T18:44:52.290Z Has data issue: false hasContentIssue false
  • English
  • Français

Matrix quadratic equations

Published online by Cambridge University Press:  17 April 2009

W.A. Coppel
W.A. Coppel
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Matrix quadratic equations have found the most diverse applications. The present article gives a connected account of their theory, and contains some new results and new proofs of known results.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 10 , Issue 3 , June 1974 , pp. 377 - 401
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Bucy, Richard S., Joseph, Peter D., Filtering for stochastic processes with applications to guidance (Interscience Tracts in Pure and Applied Mathematics, 23. Interscience [John Wiley & Sons], New York, London, Sydney, Toronto, 1968).Google Scholar
[2]Heymann, Michael, “Comments ‘On pole assignment in multi-input controllable linear systems’”, IEEE Trans. Automatic Control 13 (1968), 748–749.CrossRefGoogle Scholar
[3]Kalman, R.E., Falb, P.L., Arbib, M.A., Topics in mathematical system theory (McGraw-Hill, New York; Toronto, Ontario; London; 1969).Google Scholar
[4]Kleinman, David L., “On an iterative technique for Riccati equation computations”, IEEE Trans. Automatic Control 13 (1968), 114–115.Google Scholar
[5]Kučera, Vladimír, “A contribution to matrix quadratic equations”, IEEE Trans. Automatic Control 17 (1972), 344–347.CrossRefGoogle Scholar
[6]Lancaster, Peter, “Explicit solutions of linear matrix equations”, SIAM Rev. 12 (1970), 544–566.CrossRefGoogle Scholar
[7]Lukes, Danlard L., “Stabilizability and optimal control”, Eunkcial. Ekvac. 11 (1968), 39–50.Google Scholar
[8]Molinari, B.P., “The stabilizing solution of the algebraic Riccati equation”, SIAM J. Control 11 (1973), 262–271.CrossRefGoogle Scholar
[9]Molinari, B.P., “Equivalence relations for the algebraic Riccati equation”, SIAM J. Control 11 (1973), 272–285.Google Scholar
[10]Ostrowski, Alexander and Schneider, Hans, “Some theorems on the inertia of general matrices”, J. Math. Anal. Appl. 4 (1962), 72–84.CrossRefGoogle Scholar
[11]Reid, William T., “Riccati matrix differential equations and non-oscillation criteria for associated linear differential systems”, Pacific J. Math. 13 (1963), 665–685.CrossRefGoogle Scholar
[12]Reid, William T., “A matrix equation related to a non-oscillation criterion and Liapunov stability”, Quart. Appl. Math. 23 (1965), 83–87.CrossRefGoogle Scholar
[13]Roberts, J.D., “Linear model reduction and solution of the algebraic Riccati equation by use of the sign function”, Dep. Eng. Univ. Cambridge, Cambridge, England, Rep. CUED/B Control/TR 13, 1971.Google Scholar
[14]Roth, William E., “On the matric equation X2 + AX + XB + C = 0”, Proc. Amer. Math. Soc. 1 (1950), 586–589.Google Scholar
[15]Willems, Jan C., “Least squares stationary optimal control and the algebraic Riccati equation”, IEEE Trans. Automatic Control 16 (1971), 621–634.Google Scholar
[16]Wonham, W.M., “On a matrix Riccati equation of stochastic control”, SIAM J. Control 6 (1968), 681–697; “Erratum: On a matrix Riccati equation of stochastic control”, SIAM J. Control 1 (1969), 365.CrossRefGoogle Scholar