Semiglobal stabilization of linear systems using constrained controls: A parametric optimization approach

International Journal of Robust and Nonlinear Control

Volumn 9, Issue 8, 1999, Pages 461-484

  Solís Daun, Julio ^a   Álvarez Ramírez, José ^a   Suárez, Rodolfo ^a  

^a UNIVERSIDAD AUTÓNOMA METROPOLITANA   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

ACTUATORS; ASYMPTOTIC STABILITY; CONSTRAINT THEORY; CONTROLLABILITY; CRANES; FEEDBACK CONTROL; INERTIAL NAVIGATION SYSTEMS; LYAPUNOV METHODS; MATHEMATICAL PROGRAMMING; SYSTEM STABILITY;

PARAMETRIC PROGRAMMING; SEMIGLOBAL STABILIZATION;

LINEAR CONTROL SYSTEMS;

EID: 0033164595     PISSN: 10498923     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1239(19990715)9:8<461::AID-RNC415>3.0.CO;2-O     Document Type: Article

References (26)

1. Sontag, E. D., 'An algebraic approach to bounded controllability of linear systems', Int. J. Control, 39, 181-188 (1984).
2. Fuller, A. T., 'In-the-large stability of relay and saturated control systems with linear controllers', Int. J. Control, 10, 457-480 (1969).
3. Sussmann, H. J. and Y. Yang, 'On the stability of multiple integrators by means of bounded feedback controls', Proc. 30th IEEE Conf. Dec. Contr., Brighton, England, 1991, pp. 70-72.
4. Sontag, E. D. and H. J. Sussmann, 'Nonlinear output feedback design for linear systems with saturating controls', Proc. 29th IEEE Conf. Dec. Contr., Honolulu, HI, 1990, pp. 3414-3416.
5. Teel, A. R., 'Global stabilization and restricted tracking for multiple integrators with bounded controls', System Control Lett., 18, 165-171 (1992).
6. Sussmann, H. J., E. D. Sontag and Y. Yang, 'A general result on the stabilization of linear systems using bounded control', IEEE Trans. Automat. Control, 39, 2411-2424 (1994).
7. Suárez, R., J. Álvarez-Ramírez and J. Solís-Daun, 'Linear systems with bounded inputs: global stabilization with eigenvalue placement', Int. J. Robust Nonlinear Control, 7, 835-845 (1997).
8. 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. García (Eds), Lect. Notes Contr. Info. Sci., No. 227, Springer, London, U.K., 1997, pp. 25-38.
9. Wredenhagen, G. F. and P. R. Bélanger, 'Piecewise-linear LQ control for systems with input constraints', Automatica, 30, 403-416 (1994).
10. ∞-type controllers', Int. J. Robust. Nonlinear Control, 5, 399-411 (1995).
11. Teel, A. R., 'Semi-global stabilization of linear null controllable systems with input nonlinearities', IEEE Trans. Automat. Control, 40, 96-100 (1995).
12. Lin, Z. and A. Saberi, 'Semi-global exponential stabilization of linear systems subject to "input saturation" via linear feedbacks', System Control Lett., 21, 225-239 (1993).
13. Álvarez-Ramírez, J., R. Suárez and J. Álvarez, 'Semiglobal stabilization of multi-input linear systems with saturated linear state feedback', System Control Lett., 23, 247-254 (1994).
14. Saberi, A., Z. Lin and A. R. Teel, 'Control of linear systems with saturating actuators', IEEE Trans. Automat. Control, 41, 368-378 (1996).
15. Lin, Z., 'Semi-global stabilization of linear systems with position and rate limited actuators', System Control Lett., 30, 1-11 (1997).
16. Lin, Z., Pachter, M., Banda, S. and Y. Shamash, 'Stabilizing feedback design for linear systems with rate limited actuators', in Control of Uncertain Systems with Bounded Inputs, S. Tarbouriech and G. García (Eds), Lect. Notes Contr. Info. Sci., No. 227, Springer, London, U.K., 1997, pp. 172-186.
17. ∞-almost disturbance decoupling with internal stability for linear systems subject to input saturation', IEEE Trans. Automat. Control, 42, 992-995 (1997).
18. Morari, M. and E. Zafiriou, Robust. Process Control, Prentice-Hall, Englewood Cliffs, NJ, 1989.
19. R. Sepulchre, M. Jancovic' and P. Kokotovic', Constructive Nonlinear Control, Springer, London, U.K., 1997.
20. Byrnes, C. I., A. Isidori and J. C. Willems, 'Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear system', IEEE Trans. Automat. Control, 36, 1228-1240 (1991).
21. Lin, W., 'Global asymptotic stabilization of general nonlinear systems with stable free dynamics via passivity and bounded feedback', Automatica, 32, 915-924 (1996).
22. Fujiwara, O., 'Morse programs: a topological approach to smooth constrained optimization. I', Math. Oper. Res., 7, 602-616 (1982).
23. Luenberger, D. G., Linear and Nonlinear Programming, 2nd. edn., Addison-Wesley, Reading, MA, 1984.
24. Frankena, J. F. and R. Sivan, 'A non-linear optimal control law for linear systems', Int. J. Control, 30, 159-178 (1979).
25. Franklin, G. F., E. D. Powell and A. Emami-Naeine, Feedback Control of Dynamic Systems, Addison-Wesley, Reading, MA, 1991.
26. Ackermann, J., Robust Control: Systems with Uncertain Physical Parameters, Springer, London, U.K., 1994.