Optimal l∞ disturbance attenuation and global stabilization of linear systems with bounded control

International Journal of Robust and Nonlinear Control

Volumn 9, Issue 10, 1999, Pages 659-675

  Sznaier, Mario ^a   Suárez, Rodolfo ^b   Miani, Stefano ^c   Alvarez Ramírez, José ^b  

^a The Pennsylvania State University   (United States)

^b DEPARTAMENTO DE QUÍMICA   (Mexico)

^c UNIVERSITY OF PADOVA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL SYSTEM ANALYSIS; FEEDBACK CONTROL; NONLINEAR CONTROL SYSTEMS; OPTIMAL CONTROL SYSTEMS; STATE FEEDBACK; SYSTEM STABILITY;

BOUNDED CONTROL; DISTURBANCE ATTENUATION;

LINEAR CONTROL SYSTEMS;

EID: 0032624910     PISSN: 10498923     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1239(199908)9:10<659::AID-RNC428>3.0.CO;2-M     Document Type: Article

References (30)

1. Bernstein, D. S. and A. N. Michel, 'A chronological bibliography on saturating actuators', Int. J. Robust Nonlinear Control, Special Issue on Saturating Actuators, 5(5), 375-381 (1995).
2. Alvarez-Ramírez, J., R. Suárez and J. Alvarez, 'Semi-global stabilization of multi-input linear systems with saturated linear state feedback', Systems Control Lett., 23, 247-254 (1994).
3. Burgat, C., S. Tarbouriech and M. Klai, 'Continuous-time saturated state feedback regulators: theory and design', Int. J. Systems Sci., 25, 315-336 (1994).
4. Fuller, A. T., 'In-the-large stability of relay and saturating control systems with linear controllers', Int. J. Control, 10, 457-480 (1969).
5. Lin, Z. and A. Saberi, 'Semi-global exponential stabilization of linear systems subject to "input saturation" via linear feedbacks', Systems Control Lett., 21, 225-239 (1993).
6. Sussmann, H. J., E. Sontag and Y. Yang, 'A general result on stabilization of linear systems using bounded control', IEEE Trans. Automat. Control, 39, 2411-2424 (1994).
7. Aguirre, B., J. Alvarez-Ramírez, G. Fernandez and R. Suárez, 'First harmonic analysis of linear control systems with high gain saturating feedback', Int. J. Bifur. Chaos, to appear.
8. Komarov, V. A., Design of constrained controls for nonautonomous linear systems', Automat. Remote Control, 10, 1280-1286 (1985).
9. Suárez, J. Solis-Daun and J. Alvarez, Stabilization of linear control systems by means of bounded continuous nonlinear feedback control, Systems Control Lett., 23, 403-410 (1994).
10. Korobov, V. I., 'A general approach to the solution of the bounded control synthesis problem in a controllability problem, Math. USSR Sbornik, 37, 535-539 (1985).
11. Gavrilyako, V. M., V. I. Korobov and G. M. Sklyar, 'Designing a bounded control of dynamic systems in entire space with the aid of a controllability function', Automat. Remote Control, 11, 1484-1490 (1986).
12. Vidyasagar, M., 'Optimal rejection of persistent bounded disturbances', IEEE Trans. Automat. Control, 31(6), 527-535 (1986).
13. 1-Optimal feedback controllers for MIMO discrete-time systems', IEEE Trans. Automat. Control, AC-32, 314-322 (1987).
14. Khammash, M. and J. B. Pearson, 'Performance robustness of discrete-time systems with structured uncertainty', IEEE Trans. Automat. Control, 36, 398-412 (1991).
15. Lin, Z. and Saberi, A., 'A semi-global low-and high gain design technique for linear systems with input saturation-stabilization and disturbance rejection', Int. J. Robust Nonlinear Control, 5, 381-398 (1995).
16. p-stabilization and internal stabilization of linear systems subject to input saturation state feedback case', Systems Control Lett., 25, 219-226 (1995).
17. Chitour, Y., W. Liu and E. Sontag, 'On the continuity and incremental-gain properties of certain saturated linear feedback loops', Int. J. Robust Nonlinear Control, 5, 413-440 (1995).
18. 2 norm of single input linear systems with saturation', Proc. 33rd Conf. on Dec. and Contr., 1994, pp. 1427-1432.
19. Teel, A. R., 'Additional stability results with bounded controls', Proc. 33 IEEE CDC, Lake Buena Vista, F1., Dec. 14-16, 1994, pp. 133-137.
20. Blanchini, F. and M. Sznaier, 'Persistent disturbance rejection via static state feedback', IEEE Trans. Automat. Control, 40(6), 1127-1131 (1995).
21. 1 optimal control', Systems Control Lett., 21, 265-270 (1993).
22. ∞ gain minimization: dynamic versus static state feedback', Proc. 35th IEEE CDC, Kobe, Japan, December 1996, pp. 2395-2400.
23. Blachini, F., 'Ultimate boundedness control for discrete time uncertain systems via set induced Lyapunov functions', IEEE Trans. Automat. Control, 39(2), 428-433 (1994).
24. Gilbert, E. G. and K. T. Tan, 'Linear systems with state and control constraints: the theory and application of maximal output admissible sets', IEEE Trans. Automat. Control, 36(9), 1008-1020 (1991).
25. Gutman, P. O. and C. Cwikel, 'Admissible sets and feedback control for discrete-time linear dynamical systems with bounded controls and state', IEEE Trans. Automat. Control, AC-31(4), 373-376 (1986).
26. Alvarez-Ramírez, and R. Suárez, 'Global stabilization of discrete-time linear systems with bounded inputs', Int. J. Adapt. Control Signal Process, 10, 409-416 (1996).
27. 1 optimal controllers for linear systems', IEEE Trans. Automat. Control, AC-40(4), 694-696 (1995).
28. Blanchini, F., 'Feedback control for linear time invariant systems with state and control bounds in the presence of disturbances', IEEE Trans. Automat. Control, 35(11), 1231-1234 (1990).
29. Nagpal, K., J. Abedor and K. Poolla, 'An LMI approach to peak-to-peak gain minimization, filtering and control', Proc. 1994 American Control Conf., Baltimore, MD, June 29-July 1, pp. 742-746.
30. 2-Disturbance attenuation for linear systems with bounded controls: an ARE-based approach', in Control of Uncertain Systems with Bounded Inputs, S. Tarbouriech and G. Garcia (Eds), Springer, Berlin, (LNCIS), London, 1997.