Statistical analysis of stable FDLCP systems by parametric transfer matrices

International Journal of Control

Volumn 78, Issue 10, 2005, Pages 747-761

  Lampe, B P ^a   Obraztsov, M A ^b   Rosenwasser, E N ^b  

^a UNIVERSITY OF ROSTOCK   (Germany)

^b Maritime Technical University of Saint Petersburg   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

MATRIX ALGEBRA; STOCHASTIC CONTROL SYSTEMS; VECTORS;

FDLCP SYSTEMS; VARIANCE MATRIX;

STATISTICAL METHODS;

EID: 27944509554     PISSN: 00207179     EISSN: 13665820     Source Type: Journal    
DOI: 10.1080/00207170500149309     Document Type: Article

References (29)

1. M. Araki, Y. Ito and T. Hagiwara, "Frequency-response of sampled-data systems", Automatica, 32, pp. 483-497, 1996.
2. S. Bittanti, "The periodic Riccati equation", in Deterministic and stochastic linear-periodic systems, time series and linear systems, S. Bittanti, Ed., Berlin, New York: Springer-Verlag, 1986, pp. 141-182.
3. S. Bittanti and P. Colaneri (Eds), Preprints: IFAC workshop on periodic control systems, Como, Italy, Aug 2001.
4. P. Bolzern and P. Colaneri, "The periodic Lyapunov equation", SIAM J. Matrix Anal. Appl., 9, pp. 499-512, 1988.
5. B.F. Bykov, G.E. Vinograd, D.M. Grobman and V.V. Nemytskii, Theory of Lyapunov Indices, Moscow: Nauka, 1966 (in Russian).
6. ∞. Part I: Theoretical aspects; Part II: State feedback control", Kybernetika, 36(3), pp. 211-242; 329-350, 2000.
7. J.A. Daletskii and M.G. Krein, Stability of Solutions of Differential Equations in Banach-space, Moscow: Nauka, 1970 (in Russian).
8. D.K. Faddeev and V.N. Faddeeva, Computational Methods in Linear Algebra, Moscow: Fizmatgiz, 1960 (in Russian).
9. M. Farkas, Periodic Motions, Berlin: Springer-Verlag, 1994.
10. G.M. Fichtenholz, Course on Differential and Integral Calculus, Moscow: Fismatgis, 1959 (in Russian).
11. F.R. Gantmacher, The Theory of Matrices, Chelsea, New York, 1959.
12. M. Green and D.J.N. Limebeer, Linear Robust Control, Englewood Cliffs, NJ: Prentice-Hall, 1995.
13. P. Hartman, Ordinary Differential Equations, New York, London, Sydney: John Wiley & Sons, 1964.
14. G.W. Hill, "On the part of the lunar perigee which is a function of the mean motions of the sun and the moon", Acta Mathematica, 8, pp. 1-36, 1886.
15. H. Kwakernaak and R. Sivan, Linear Optimal Control Systems, New York: Wiley-Interscience, 1972.
16. 2-norm of finite dimensional linear time-periodic systems", in Proc. IFAC Workshop on Periodic Control Systems, Como, Italy, Aug. 2001, pp. 9-14.
17. B.P. Lampe and E.N. Rosenwasser, "Operational description and statistical analysis of linear periodic systems on the unbounded interval -∞ < t < ∞", European J. Control, 9(5), pp. 508-521, 2003.
18. C. Moler and C. van Loan, "Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later", SIAM Review, 45(1), pp. 3-49, 2003.
19. PSYCO, IFAC workshop on periodic control systems, Yokohama, Japan, 2004.
20. E.N. Rosenwasser, Lyapunov Indices in Linear Control Theory, Moscow: Nauka, 1977 (in Russian).
21. E.N. Rosenwasser and B.P. Lampe, Computer Controlled Systems - Analysis and Design with Process-orientated Models, London, Berlin, Heidelberg: Springer-Verlag, 2000.
22. A. Varga, "On solving periodic differential matrix equations with application to periodic system norms computation", in Proc. IEEE CDC/ECC, Sevilla, E, Dec 2005. (subm.).
23. N. Wereley, "Analysis and control of linear periodically time varying systems", PhD thesis, Dept. Aeronautics and Astronautics, MIT (1991).
24. N. Wereley and S. Hall, "Frequency response of linear time-periodic systems", in Proc. 29th IEEE Conf. Decision Contr, Honolulu, Hawaii, 1990, pp. 3650-3655.
25. J.H. Wilkinson, The Algebraic Eigenvalue Problem, Oxford: Clarendon Press, 1965.
26. V.A. Yakubovich and V.M. Starzhinskii, Linear Differential Equations with Periodic Coefficients, Vol. 1, New York: John Wiley & Sons, 1975.
27. 2-performance of continuous periodically time-varying controllers", Syst. Contr. Lett, 32, pp. 209-221, 1997.
28. 2 norm of linear continuous-time periodic systems", in Prepr. IFAC Workshop on Periodic Control Systems, Como, Italy, 2001, pp. 3-8.
29. J. Zhou, T. Hagiwara and M. Araki, "Trace formula of linear continuous-time periodic systems via the harmonic Lyapunov equation", Int. J. Control, 76(5), pp. 488-500, 2003.