Abstract
We describe the connection between a generalized algebraic Riccati equation and the corresponding generalized algebraic Riccati system and Kalman-Popov-Yakubovich system. Moreover, we present an iterative procedure for constructing its stabilizing solution.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-0-387-35690-7_44
Chapter PDF
Similar content being viewed by others
Keywords
References
Ahlbrandt, C. D.; Peterson, A. C.: Discrete Hamiltonian systems, Kluwer Academic Publishers Group, Dordrecht, 1996.
Ait Rami, M.; Chen, X.; Moore, J. B.; Zhou, X. Y.: Solvability and asymptotic behavior of generalized Riccati equations arising in indefinite stochastic LQ controls, IEEE Trans. Automat. Control 46 (2001), 428–440.
Ait Rami, M.; Moore, J. B.; Zhou, X. Y.: Indefinite stochastic linear quadratic control and generalized differential Riccati equations, Preprint.
Ait Rami, M.; Zhou, X. Y.: Linear matrix inequalities, Riccati equations, and indefinite stochastic linear quadratic controls, IEEE Trans. Automat. Control 45 (2000), 1131–1143.
Chen, S.; Li, X.; Zhou, X. Y.: Stochastic linear quadratic regulators with indefinite control weight costs, SIAM J. Control Optim. 36 (1998), 1685–1702.
Chen, S.; Yong, J.: Stochastic linear quadratic optimal control problems, Appl. Math. Optim. 43 (2001), 21–45.
Chen, S.; Zhou, X. Y.: Stochastic linear quadratic regulators with indefinite control weight costs II, SIAM J. Control Optim. 39 (2000), 1065–1081.
Damm, T.; Hinrichsen, D.: Newton’s method for a rational matrix equation occuring in stochastic control, Linear Algebra Appl. 332 /334 (2001), 81–109.
Dragan, V.; Morozan, T.: Stability and robust stabilization to linear stochastic systems described by differential equations with markovian jumping and multiplicative white noise, Stochastic Analysis, 20, no. 1, 2002, 33–92.
Dragan, V.; Morozan, T.: Systems of matrix rational differential equations arising in connection with linear stochastic systems with markovian jumping, Preprint No. 9/2000, Institutul de Matematicâ al Academiei Române (2000); to appear in J. Differential Equ., 2003.
Feng, X.; Loparo, K. A.; Ji, Y.; Chizeck, H. J.: Stochastic stability properties of jump linear systems, IEEE Trans. Automat. Control 37 (1992), 38–53.
Fragoso, M. D.; Costa, O. L. V.; de Souza, C. E.: A new approach to linearly perturbed Riccati equations arising in stochastic control, Appl. Math. Optim. 37 (1998), 99–126.
Freiling, G.; Hochhaus, A.: Properties of the solutions of rational matrix difference equations. Advances in difference equations, IV, Comput. Math. Appl.,to appear.
Freiling, G.; Hochhaus, A.: On a class of rational matrix differential equations arising in stochastic control, Linear Algebra Appl.,to appear.
Halanay, A.; Samuel, J.: Differential equations, discrete systems and control, Kluwer Academic Publishers, Dordrecht, 1997.
Harville, D. A.: Matrix algebra from a statistician’s perspective, Springer-Verlag, New York, 1997.
Ionescu, V.; Oarâ, C.; Weiss, M.: Generalized Riccati theory and robust control, John Wiley und Sons, Ltd., Chichester, 1999.
Yong, J.; Zhou, X. Y.: Stochastic controls, Springer-Verlag, New York, 1999.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 IFIP International Federation for Information Processing
About this paper
Cite this paper
Freiling, G., Hochhaus, A. (2003). About a Generalized Algebraic Riccati Equation. In: Barbu, V., Lasiecka, I., Tiba, D., Varsan, C. (eds) Analysis and Optimization of Differential Systems. SEC 2002. IFIP — The International Federation for Information Processing, vol 121. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35690-7_17
Download citation
DOI: https://doi.org/10.1007/978-0-387-35690-7_17
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-4506-1
Online ISBN: 978-0-387-35690-7
eBook Packages: Springer Book Archive