Riccati equation theory for Pritchard-Salamon systems: A Popov function approach

IMA Journal of Mathematical Control and Information

Volumn 14, Issue 1, 1997, Pages 45-83

  Weiss, Martin ^a  

^a UNIVERSITY OF GRONINGEN   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL THEORY; DISCRETE TIME CONTROL SYSTEMS; MATHEMATICAL OPERATORS; PROBLEM SOLVING; THEOREM PROVING;

POPOV FUNCTION METHOD; PRITCHARD SALAMON SYSTEMS;

RICCATI EQUATIONS;

EID: 0030677539     PISSN: 02650754     EISSN: None     Source Type: Journal    
DOI: 10.1093/imamci/14.1.45     Document Type: Article

References (17)

1. ANDERSON, B., & VONGPANITLERD S., (1973). Network Analysis and Synthesis: A Modern systems Theory Approach. Prentice Hall Network Series. Englewood Cliffs, New Jersey: Prentice-Hall, Inc.
2. AUBIN, J., (1979). Applied Functional Analysis. New York: Wiley.
3. BART, H., GOHBERG, I., & KAASHOEK M., (1986). Wiener-Hopf factorization, inverse Fourier transforms and exponentially dichotomous operators. Journal of Functional Analysis 68(1), 1-42.
4. CURTAIN, R., LOGEMAN, H., TOWNLEY, S., & ZWART H., (1993). Well-posedness, stabilizability and admissibility for Pritchard-Salamon systems. Journal of Mathematical Systems, Estimation and Control, to appear.
5. CURTAIN, R., & RODRÍGUEZ, A., (1992). Necessary and sufficient conditions for J-spectral factorizations with a J-lossless property for infinite-dimensional systems in continuous and discrete time. Report W-9217, Department of Mathematics, University of Groningen, POB 800, 9700 AV Groningen, The Netherlands.
6. CURTAIN, R., & ZWART, H., (1993). An introduction to infinite-dimensional linear systems theory. in preparation.
7. CURTAIN, R., & ZWART, H., (1994). The Nehari problem for the Pritchard-Salamon class of infinite-dimensional linear systems: a direct approach. J. of Operator Theory and Integral Theory 18, 130-153.
8. GLOVER, K., LIMEBEER, D., DOYLE, J., KASENALLY, E., & SAFONOV, M., (1991). A characterization of all solutions to the four block general distance problem. SIAM J. on Control and Optimization 29, 283-324.
9. IONESCU, V., & WEISS, M., (1993a). Continuous and discrete-time Riccati theory: A Popov function approach. Linear Algebra and Its Applications 193, 173-209.
10. ∞-control problem. Int.J.Control 57(1), 141-195.
11. JUANG, J.-C., & JONCKHEERE, E., (1988). On computing the spectral radius of the Hankel plus Toeplitz operator. IEEE Trans. Autom. Control 33(11), 1053-1059.
12. KREYSZIG, E., (1978) Introductory Functional Analysis with Applications. New York: Wiley.
13. PRITCHARD, A., & SALAMON, D., (1987). The linear quadratic optimal control problem for infinite-dimensional systems with unbounded input and output operators. SIAM J. Control and Optimization 25, 121-144.
14. TAYLOR, A., & LAY, D., (1979). Introduction to Functional Analysis. New York: John Wiley & Sons.
15. ∞ control for infinite-dimensional systems: a state-space approach. Ph. D. thesis, University of Groningen, Mathematics Department, P.O.Box 800, 9700 AV Groningen , Netherlands.
16. WEISS, M., (1993). Necessary and sufficient conditions for the existence of the stabilizing solution of the Riccati equation in a Hilbert space: a Popov function approach. Report W-9311, Department of Mathematics, University of Groningen, POB 800, 9700 AV Groningen, The Netherlands. submitted to Journal of Mathematical Systems, Estimation and Control.
17. ZABCZYK, J., (1976). Remarks on the algebraic Riccati equation in Hilbert space. Appl. Math. & Opt. 2(3), 251-258.