Spectral characteristics and eigenvalues computation of the harmonic state operators in continuous-time periodic systems

Systems and Control Letters

Volumn 53, Issue 2, 2004, Pages 141-155

  Zhou, Jun ^a   Hagiwara, Tomomichi ^a   Araki, Mituhiko ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

Eigenvalue computation; Fredholm operator; Periodic; Spectrum; Stability

Indexed keywords

FOURIER COEFFICIENTS; FREEDHOLM OPERATOR; PERIODIC; SPECTRUM;

ASYMPTOTIC STABILITY; CALCULATIONS; EIGENVALUES AND EIGENFUNCTIONS; FEEDBACK; FOURIER TRANSFORMS; HARMONIC ANALYSIS; SPECTRUM ANALYZERS; THEOREM PROVING; VECTORS;

TIME VARYING SYSTEMS;

EID: 4344682592     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2004.03.002     Document Type: Article

References (29)

1. Araki M., Hagiwara T. Pole assignment by multirate sampled-data output feedback. Internat. J. Control. 44:1986;1661-1673.
2. Araki M., Ito Y., Hagiwara T. Frequency response of sampled-data systems. Automatica. 32:1996;483-497.
3. Bolzern P., Colaneri P., Scattolini R. Zeros of discrete-time linear periodic systems. IEEE Trans. Automat. Control. AC-31:1986;1057-1058.
4. Böttcher A., Silbermann B. Analysis of Toeplitz Operators. 1990;Springer, Berlin.
5. Churchill R.V. Fourier Series and Boundary Value Problems. 2nd Edition:1963;McGraw-Hill, New York.
6. Conway J.B. A Course in Functional Analysis. 2nd Edition:1990;Springer, New York.
7. Farkas M. Periodic Motions. 1994;Springer, New York.
8. I. Gohberg, S. Goldberg, M.A. Kaashoek, Classes of Linear Operators, Vol. I, Birkhäuser, Basel, 1990.
9. I. Gohberg, S. Goldberg, M.A. Kaashoek, Classes of Linear Operators, Vol. II, Birkhäuser, Basel, 1993.
10. Grasselli O.M., Longhi S. Zeros and poles of linear periodic multivariable discrete-time systems. Circuits Systems Signal Process. 7:1988;361-380.
11. T. Hagiwara, M. Araki, Properties of limiting zeros of sampled-data systems, in: Proceedings of the 18th SICE Symposium on Control Theory, Kobe, 1989, pp. 241-246 (in Japanese).
12. 2 analysis and synthesis of sampled-data systems IEEE Trans. Automat. Control. 40(8):1995;1411-1421.
13. ∞ -norm of a sampled-data system Systems Control Lett. 25(4):1995;281-288.
14. Halanay A. Differential Equations: Stability, Oscillations, Time Lags. 1966;Academic Press, New York.
15. Horn R.A., Johnson C.R. Topics in Matrix Analysis. 1991;Cambridge University Press, New York.
16. Lukes D.L. Differential Equations: Classical to Controlled. 1982;Academic Press, New York.
17. MacFarlane A.G.J., Karcanias N. Poles and zeros of linear multivariable systems. a survey of the algebraic, geometric and complex-variable theory Internat. J. Control. 22:1976;33-74.
18. Myint-U T. Ordinary Differential Equations. 1978;North-Holland, Amsterdam.
19. Naylor A.W., Sell G.R. Linear Operator Theory in Engineering and Science. 1982;Springer, New York.
20. Nicolao G.D., Ferrari-Terecate G. On the zeros of discrete-time linear periodic systems. Circuits Systems Signal Process. 16:1997;703-718.
21. Nicolao G.D., Ferrari-Terecate G., Pinzoni S. Zeros of continuous-time linear periodic systems. Automatica. 34:1998;1651-1655.
22. Rosenbrock H.H. State-space and Multivariable Theory. 1970;Nelson, London.
23. Rudin W. Real and Complex Analysis. 3rd Edition:1987;McGraw-Hill, New York.
24. Schrader C.B., Sain M.K. Research on system zeros. a survey Internat. J. Control. 50:1989;1407-1433.
25. N.M. Wereley, Analysis and control of linear periodically time varying systems, Ph.D. Thesis, Department of Aeronautics and Astronautics, MIT, 1990.
26. Zhou J., Hagiwara T. Existence conditions and properties of frequency response operators of continuous-time periodic systems. SIAM J. Control Optim. 40:2002;1867-1887.
27. ∞ norm computations of linear continuous-time periodic systems via the skew analysis of frequency response operators Automatica. 38:2002;1381-1387.
28. ∞ performance in linear continuous-time periodic systems, in: Proc. 42nd IEEE Conf. on Decision and Control, Mani, HI, 2003, pp. 1795-1800.
29. Zhou J., Hagiwara T., Araki M. Stability analysis of continuous-time periodic systems via the harmonic analysis. IEEE Trans. Automat. Control. 47:2002;292-298.