Stabilization of bilinear systems via linear state feedback control

2007 Mediterranean Conference on Control and Automation, MED

Volumn , Issue , 2007, Pages

  Amato, Francesco ^a   Cosentino, Carlo ^a   Merola, Alessio ^a  

^a UNIVERSITY MAGNA GRAECIA OF CATANZARO   (Italy)

Author keywords

Bilinear systems; Domain of attraction; LMIs; Stabilization; State feedback control

Indexed keywords

CLOSED LOOP CONTROL SYSTEMS; CLOSED LOOP SYSTEMS; CONTROL SYSTEMS; CONTROL THEORY; DISCRETE TIME CONTROL SYSTEMS; FEEDBACK; FEEDBACK CONTROL; INDUSTRIAL ENGINEERING; LINEAR CONTROL SYSTEMS; LINEAR MATRIX INEQUALITIES; MATRIX ALGEBRA; NEURAL NETWORKS; NONLINEAR CONTROL SYSTEMS; STATE SPACE METHODS;

ASYMPTOTICALLY STABLE; BILINEAR SYSTEMS; CONTROL AND AUTOMATION; CONTROLLER DESIGNS; CONVEX OPTIMIZATION PROBLEMS; DOMAIN OF ATTRACTION; EQUILIBRIUM POINTS; LINEAR STATE FEEDBACK CONTROL; LMIS; POLYTOPE; STABILIZATION; STATE FEEDBACK CONTROL; STATE SPACES;

STATE FEEDBACK;

EID: 50249101185     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/MED.2007.4433740     Document Type: Conference Paper

References (18)

1. C. Bruni, G. Di Pillo, and G. Koch, "Bilinear Systems: An Appealing Class of "Nearly Linear" Systems in Theory and Applications," IEEE Transactions on Automatic Control, vol. 19, pp. 334-348, 1974.
2. R. R. Mohler, Bilinear Control Processes. Academic Press, New York, NY, 1973.
3. R. R. Mohler, C. Bruni, and A. Gandolfi, "A Systems Approach to Immunology," Proceedings of the IEEE, vol. 68, pp. 964-990, 1980.
4. L. Guo and H. Schwarz, "A Control Scheme for Bilinear Systems and Application to a Secondary Controlled Hydraulic Rotary Drive," in Proc. of the 28th IEEE Conference on Decision and Control, Tampa, Florida, 1989.
5. R. R. Mohler and A. Y. Khapalov, "Bilinear Control and Application to Flexible a.c. Transmission Systems," Journal of Optimization Theory and Applications, vol. 105, pp. 621-637, 2000.
6. R. Longchamp, "Stable Feedback Control of Bilinear Systems," IEEE Transactions on Automatic Control, vol. 25, pp. 302-306, 1980.
7. P.-O. Gutman, "Stabilizing Controllers for Bilinear Systems," IEEE Transactions on Automatic Control, vol. 26, pp. 917-922, 1981.
8. D. E. Koditschek and K. S. Narendra, "Stabilizability of Second-Order Bilinear Systems," IEEE Transactions on Automatic Control, vol. 28, pp. 987-989, 1983.
9. A. Y. Khapalov and R. R. Mohler, "Reachable Sets and Controllability of Bilinear Time-Invariant Systems: A Qualitative Approach," IEEE Transactions on Automatic Control, vol. 41, pp. 1342-1346, 1996.
10. _, "Asymptotic Stabilization of the Bilinear Time-Invariant System via Piecewise-Constant Feedback," Systems and Control Letters, vol. 33, pp. 47-54, 1998.
11. Z. Aganovic and Z. Gajic, "The successive approximation procedure for finite-time optimal control of bilinear systems," IEEE Transactions on Automatic Control, vol. 39, pp. 1932-1935, 1994.
12. ∞ State Feedback Control Methods for Bilinear Systems," IEE Proc.-Control Theory Appl., vol. 152, pp. 553-559, 2005.
13. G. Lu, Y. Zheng, C. Zhang, and X. Yu, "Global Asymptotic Stabilization of MIMO Bilinear Systems with Undamped Natural Response," in Proc. of the 37th IEEE Conference on Decision and Control, Tampa, Florida, 1998.
14. H. Jerbi, "Global Feedback Stabilization of New Class of Bilinear Systems," Systems and Control Letters, vol. 42, pp. 313-320, 2001.
15. H. K. Khalil, Nonlinear Systems. MacMillan, 1992.
16. F. Garofalo, G. Celentano, and L. Glielmo, "Stability robustness of interval matrices via quadratic Lyapunov forms," IEEE Transactions on Automatic Control, vol. 38, pp. 281-284, 1993.
17. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. SIAM Press, 1994.
18. M. Chilali, P. Gahinet, and P. Apkarian, "Robust pole Placement in LMI Regions," IEEE Transactions on Automatic Control, vol. 44, pp. 2257-2270, 1999.