Reformulating negative imaginary frequency response systems to bounded-real systems

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2008, Pages 322-326

  Lanzon, Alexander ^a   Song, Zhuoyue ^a   Petersen, Ian R ^b  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

^b UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Bounded real; Lightly damped systems; Negative imaginary frequency response; Passivity; Positive real; Small gain theorem

Indexed keywords

CLOSED LOOP SYSTEMS; CONTROLLERS; FREQUENCY RESPONSE; PLASMA INTERACTIONS;

BOUNDED REAL; IMAGINARY FREQUENCY; LIGHTLY DAMPED SYSTEMS; PASSIVITY; POSITIVE REAL; SMALL GAIN THEOREM;

CLOSED LOOP CONTROL SYSTEMS;

EID: 62949122991     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2008.4738624     Document Type: Conference Paper

References (17)

1. K. Zhou, and J. C. Doyle and K. Glover, Robust and Optimal Control, Prentice-Hall, Inc. 1996.
2. ∞ controller synthesis, IEEE Transactions on Automatic Control, vol. 39, no. 4, 1994, pp 824-831.
3. A. Lanzon and I. R. Petersen, Stability robustness of a feedback interconnection of systems with negative imaginary frequency response, IEEE Transactions on Automatic Control, In Press.
4. D. Angeli, Systems with counterclockwise input-output dynamics, IEEE Transactions on Automatic Control, vol. 51, no. 7, 2006, pp 1130-1143.
5. M. G. Safonov, E. A. Jonckheere, M. Vermaj and D. J. N. Limebeer, Synthesis of positive real multivariable feedback systems, International Journal of Control, vol. 45, no. 3, 1987, pp 817-842.
6. W. Sun, P. P. Khargonekar and D. Shim, Solution to the Positive Real Control Problem for Linear Time-Invariant Systems, IEEE Transactions on Automatic Control, vol. 39, no. 10, 1994, pp 2034-2046.
7. L. Turan, M. G. Safonov, and C. H. Huang, Synthesis of Positive Real Feedback Systems: A Simple Derivation via Parrott's Theorem, IEEE Transactions on Automatic Control, vol. 42, no. 8, 1997, pp 1154-1157.
8. C. J. Goh and T. K. Caughey, On the stability problem caused by finite actuator dynamics in the collocated control of large space structures, International Journal of Control, vol. 41, no. 3, 1985, pp 787-802.
9. J. L. Fanson and T. K. Caughey, Positive Position Feedback Control for Large Space Structures, AIAA Journal, vol. 28, no. 4, 1990, pp 717-724.
10. S. O. R. Moheimani, and B. J. G. Vautier and B. Bhikkaji, Experimental Implementation of Extended Multivariable PPF Control on an Active Structure, IEEE Transactions on Control Systems Technology, vol. 14, no. 3, 2006, pp 443-455.
11. A. Lanzon and I. R. Petersen, A modified positive-real type stability condition, in Proceedings of the 2007 European Control Conference, Jul 2007, pp 3912-3918.
12. H. Khalil, Nonlinear Systems, 2nd ed. Prentice-Hall, Inc. 1996.
13. M. Green and D. J. N. Limebeer, Linear Robust Control, Prentice-Hall, Inc. 1995.
14. ∞ control problem: a state space approach, Department of Mathematics and Computing Science, Eindhoven University of Technology, The Netherlands, 1990.
15. ∞ norms, IEEE Transactions on Automatic Control, vol. 35, no. 10, 1990, pp 1090-1099.
16. ∞ control by state feedback for plants with zeros on the imaginary axis, SIAM Journal of Control and Optimization, vol. 30, no. 1, 1991, pp 123-142.
17. ∞ Control, International Journal of Robust and Nonlinear Control, vol. 4, no. 4, 1994, pp 421-448.