Control of general dynamic systems with periodically varying parameters via liapunov-floquet transformation

Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME

Volumn 116, Issue 4, 1994, Pages 650-658

  Sinha, S C ^a   Joseph, P ^a  

^a AUBURN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHEBYSHEV APPROXIMATION; CONTROL EQUIPMENT; CONTROL THEORY; FEEDBACK CONTROL; LYAPUNOV METHODS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; OPTIMAL CONTROL SYSTEMS; POLES AND ZEROS; POLYNOMIALS; SYSTEM STABILITY;

LIAPUNOV-FLOQUET TRANSFORMATION; PERIODICALLY VARYING PARAMETERS; POLE PLACEMENT; STATE TRANSITION MATRICES;

LINEAR CONTROL SYSTEMS;

EID: 0028714187     PISSN: 00220434     EISSN: 15289028     Source Type: Journal    
DOI: 10.1115/1.2899264     Document Type: Article

References (32)

1. Alfhaid, M. S., and Lee Gordan K. F., 1988, “Pole Assignment in Linear Time-Varying Systems Using State Feedback,” 22nd Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, Oct 31-Nov 2, 241-245.
2. Alfhaid, M. S., 1988, “Pole Assignment in Linear Time-Varying Systems Using State and Output Feedback,” Ph.D dissertation, Colorado State University.
3. Bellman, R., 1970, Introduction to Matrix Analysis, McGraw-Hill, New York, p. 235.
4. Bellman, R., 1970, Nonlinear Analysis, Vol. 1, Academic Press, New York.
5. Pandiyan, R., Bibb, J. S., and Sinha, S. C., 1993, "Liapunov-Floquet Transformation: Computation and Applications to Periodic Systems,” Proceedings of the 14th Biennial Conference on Mechanical Vibration and Noise, Albuquerque, NM, Sept. 19-22, DE-Vol. 56, pp. 337-348.
6. S. C. Sinha and R. M. Evan-Iwanowski, eds., Also to appear in the ASME Journal of Vibrations and Acoustics.
7. Bittanti S., Colaneri P., and Guardabassi G., 1986, “Analysis of the Periodic Lyapunov and Ricatti Equations via Canonical Decompositions,” SIAM J. of Control and Optimization, Vol. 24, pp. 1138-1148.
8. Calico, R. A. and Wiesel, W. E., 1984, “Control of Time-Periodic Systems,” J. Guidance, Control and Dynamics, Vol. 7, No. 6, pp. 671-676.
9. Calise, A. J., Wasikowski, M. E. and Schrage, D. P., 1992, “Optimal Output Feedback for Linear Time-Periodic Systems,” Journal of Guidance, Control and Dynamics, Vol. 15, No. 2, pp. 416-423.
10. Coddington, E. A. and Levinson, N., 1955, Theory of Ordinary Differential Equations, McGraw-Hill, New York.
11. D’Angelo, H., 1970, Linear Time-Varying Systems: Analysis and Synthesis, Allyn and Bacon, Boston, MA.
12. Floquet, G., 1883, “Sur Les Equations Differentiales Linearires a Coefficients Périodiques,” Annales Scientifiques de l’Ecole Normale superieue, Series 2, Vol. 12, pp. 47-88.
13. Follinger, O., 1978, “Design of Time-Varying System by Pole Assignment,” Regelungstechink, Vol. 26, No. 6, pp. 85-95.
14. Hac A. and Tomizuka M., 1990, “Application of Learning Control to Active Damping of Forced Vibration for Periodically Time Variant Systems,” ASME Journal of Vibrations and Acoustics, Vol. 112, 489-496.
15. Joseph, P., Pandiyan, R. and Sinha, S. C., 1993, “Optimal Control of Mechanical Systems Subjected to Periodic Loading via Chebyshev Polynomials,” Optimal Control, Applications and Methods, Vol. 14, pp. 75-90.
16. Kwakemaak, H., and Sivan, R., 1972, Linear Optimal Control Systems, Wiley Interscience, New York.
17. Leipholz, H., 1972, Stability Theory, Academic Press, New York.
18. Lovass-Nagy V., Miller R. J. and Powers D. L., 1978, “An Introduction to the Application of the Simplest Matrix-Generalized Inverse in System Science,” IEEE Trans. Circuits Syst., Vol. CAS-25, pp. 766-771.
19. Lukes, D. L., 1982, Differential Equations: Classical to Controlled, Academic Press, New York.
20. Mathieu, E., 1868, “Mémoire Sur le Mouvement Vibratoire de Une Membrane de Membrane de Form Elliptique,” J. Math Pures et Appliquée, Vol. 137, pp. 2-13.
21. Mohler, R. H., 1991, Nonlinear Systems, Volume 1: Dynamics and Control, Prentice Hall.
22. Nashed, M. Z., 1976, Generalized Inverses and Applications, Academic Press, New York.
23. Nishimura T., 1972, “Spectral Factorization in Periodically Time-Varying Systems and Application to Navigation Problem,” J. Spacecraft, Vol. 9, No. 7, pp. 540-546.
24. O’Reilly, J., 1983, Observers for Linear Systems, Academic Press, London.
25. Poincare, H., 1899, Les Méthodes Nouvelles de la Mécanique Celeste, 3 Vols., Gauthier-Villars, Paris.
26. Sinha, S. C., and Wu, Der-Ho, 1991, “An Efficient Computational Scheme for the Analysis of Periodic Systems,” J. Sound and Vibration, Vol. 151, pp. 91-117.
27. Sinha, S. C. and Juneja, V., 1991, “An Approximate Analytical Solution for Systems with Periodic Coefficients via Symbolic Computation,” AIAA/ASME/ASCE/AHS/ASC 32nd Structures, Structural Dynamics and Material Conference, A collection of papers, Part 1, pp. 790-797.
28. Sommer, R., 1979, “Design of Nonlinear Time-Varying System by Pole Assignment,” Regelungstechink, Vol. 27, No. 12, pp. 393-399.
29. Verhulst, F., 1990, Nonlinear Differential Equations and Dynamical Systems, Springer-Verlag, Berlin, Heidelberg.
30. Wu, Der-Ho, 1991, “Development of an Efficient Computational Technique for the Analysis of Linear Dynamic Systems with Periodically Varying Parameters,” Ph.D thesis, Auburn University, Auburn, AI.
31. Wu, Min-Yen, 1978; “Transformation of a Linear Time-Varying System Into a Linear Time-Invariant One,” Int. J. Control, Vol. 27, No. 4, pp. 589-602.
32. Yakubovich, V. A. and Starzhinskii, V. M., 1975, Linear Differential Equations with Periodic Coefficients, Vols. I and II, Halsted Press, Wiley, New York.