A review of the matrix Riccati equation. (English) Zbl 0279.49015


49J99 Existence theories in calculus of variations and optimal control
15A24 Matrix equations and identities
93E10 Estimation and detection in stochastic control theory
Full Text: EuDML


[1] M. Athans P. L. Falb: Optimal Control. McGraw-Hill, New York 1966. · Zbl 0186.22501
[2] R. W. Bass: Machine Solution of High-Order Matrix Riccati Equations. Douglas paper 4538.
[3] R. Bellman: Dynamic Programming. Princeton University Press, Princeton, N. Y. 1957. · Zbl 0995.90618
[4] S. P. Bingulac M. R. Stojić N. Ćuk: On an Iterative Solution of Time-Invariant Riccati Equation. Prepr. JACC, St. Louis, Miss., 1971, 178-182.
[5] T. R. Blackburn: Solution of the Algebraic Matrix Equation Via Newton-Raphson Iteration. Prepr. JACC, Ann Arbor, Mich., 1968, 940-945.
[6] R. W. Brockett: Finite Dimensional Linear Systems. John Wiley, New York 1970. · Zbl 0216.27401
[7] A. E. Bryson, Yu-Chi Ho: Applied Optimal Control. Bleisdell, Waltham, Mass. 1969.
[8] R. S. Bucy: Global Theory of the Riccati Equation. J. Comp. System Sci. 1 (December 1967), 4, 349-361. · Zbl 0155.14403
[9] R. S. Bucy P. D. Joseph: Filtering for Stochastic Processes with Applications to Guidance. Interscience, New York 1968. · Zbl 0174.21903
[10] J. J. O’Donnell: Asymptotic Solution of the Matrix Riccati Equation of Optimal Control. Proc. 4th Ann. Allerton Conf. Circuit and Syst. Theory, Urbana, III., 1966, 577-586.
[11] S. E. Dreyfus: Dynamic Programming and the Calculus of Variations. Academic Press, New York 1965. · Zbl 0193.19401
[12] A. F. Fath: Computational Aspects of the Linear Optimal Regular Problem. Trans. IEEE AC-14 (October 1968), 547-550.
[13] M. L. J. Hautus: Stabilization, Controllability and Observability of Linear Autonomous Systems. Nederl. Akad. Wetensch., Proc. Ser. A73 (1970), 448-455. · Zbl 0212.47302
[14] K. L. Hitz: Relations Between Continuous-Time and Discrete-Time Quadratic Minimization. Ph. D. Thesis, The University of Newcastle, Australia, 1970.
[15] R. E. Kalman: Contributions to the Theory of Optimal Control. Bol. Soc. Mat. Max. J (1961), 102-119.
[16] R. E. Kalman: When Is a Linear Control System Optimal?. Trans. ASME, J. Basic Engr. 86D (March 1964), 51-60.
[17] R. E. Kalman R. S. Bucy: New Results in Linear Prediction and Filtering Theory. Trans. ASME, J. Basic Engr. 83D (1961), 95-100.
[18] R. E. Kalman T. S. Englar: A Users Manual for the Automatic Synthesis Program. NASA Rept. CR-475, June 1966.
[19] R. E. Kalman P. L. Falb M. A. Arbib: Topics in Mathematical System Theory. McGraw-Hill, New York, 1969. · Zbl 0231.49001
[20] D. L. Kleinman: On the Linear Regulator Problem and the Matrix Riccati Equation. MIT Electronic Systems Lab., Cambridge, Mass, Rept. ESL-R-271, June 1966.
[21] D. L. Kleinman: On an Iterative Technique for Riccati Equation Computations. Trans. IEEE AC-13 (February 1968), 114-115.
[22] V. Kučera: A Contribution to Matrix Quadratic Equations. Trans. IEEE AC-17 (June 1972), 344-347.
[23] V. Kučera: On Nonnegative Definite Solutions to Matrix Quadratic Equations. Proc. 5th IFAC Congress Vol. 4, Paris, 1972. Also Automatica 7 (July 1972), 413-423.
[24] V. Kučera: The Discrete Riccati Equation of Optimal Control. Kybernetika 8 (1972), 430-447.
[25] J. J. Levin: On the Matrix Riccati Equation. Trans. Am. Math. Soc. 10 (1959), 519-524. · Zbl 0092.07803
[26] K. Mårtensson: On the Matrix Riccati Equation. Information Sci. 3 (1971), 1, 17-49. · Zbl 0206.45602
[27] A. G. J. McFarlane: An Eigenvector Solution of the Linear Optimal Regulator Problem. J. Electron. Contr. 14
[28] B. P. Molinari: The Stabilizing Solution of the Matrix Quadratic Equation. To appear in SIAM J. Control 10 (1972). · Zbl 0234.34004
[29] L. S. Pontryagin at al.: The Mathematical Theory of Optimal Processes. Interscience, New York 1961.
[30] J. E. Potter: Matrix Quadratic Solutions. SIAM J. Appl. Math. 14 (May 1966), 3, 496-501. · Zbl 0144.02001
[31] J. D. Roberts: Linear Model Reduction and Solution of the Algebraic Riccati Equation by Use of the Sign Function. To appear in Trans. IEEE AC-17 (1972).
[32] A. P. Sage: Optimum Systems Control. Prentice-Hall, Englewood Cliffs, N. J. 1968. · Zbl 0192.51502
[33] V. Strejc: State Space Synthesis of Discrete Linear Systems. Kybernetika 8 (1972), 83-113. · Zbl 0254.93028
[34] D. R. Vaughan: A Negative Exponential Solution for the Matrix Riccati Equation. Trans. IEEE AC-14 (February 1969), 72-75.
[35] W. M. Wonham: On Pole Assignment in Multi-Input Controllable Linear Systems. Trans. IEEE AC-12 (December 1967), 660-665.
[36] W. M. Wonham: On a Matrix Riccati Equation of Stochastic Control. SIAM J. Control 6 (1968), 4, 681-698. · Zbl 0182.20803
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