Guaranteed domains of attraction for multivariable luré systems via open Lyapunov surfaces

International Journal of Robust and Nonlinear Control

Volumn 7, Issue 10, 1997, Pages 935-949

  Haddad, Wassim M ^a   Kapila, Vikram ^b   Chellaboina, Vijaya Sekhar ^a  

^a Georgia Institute of Technology   (United States)

^b POLYTECHNIC UNIVERSITY   (United States)

Author keywords

Absolute stability; Domains of attraction; Lyapunov surfaces; Multivariable systems; Popov criterion; Stability regions

Indexed keywords

FEEDBACK; LYAPUNOV METHODS; NONLINEAR CONTROL SYSTEMS; SET THEORY; STABILITY CRITERIA; SYSTEM STABILITY;

MULTIVARIABLE LURE SYSTEMS; POPOV CRITERION;

MULTIVARIABLE CONTROL SYSTEMS;

EID: 0031257341     PISSN: 10498923     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1239(199710)7:10<935::AID-RNC255>3.0.CO;2-B     Document Type: Article

References (18)

1. Aizerman, M. A. and F. R. Gantmacher, Absolute Stability of Regulator Systems, Holden-Day Inc., San Francisco, 1983.
2. Lefschetz, S., Stability of Nonlinear Control Systems, Academic Press, New York, 1965.
3. Popov, V. M., 'Absolute stability of nonlinear systems of automatic control', Automat. Rem. Contr., 22, 628-629 (1967).
4. Popov, V. M., Hyperstability of Control Systems, Springer, New York, 1973.
5. Chiang, H.-D. and J. S. Thorp, 'Stability regions of nonlinear dynamical systems: A constructive methodology', IEEE Trans. Automat. Control, 34, 1229-1241 (1989).
6. Khalil, H. K., Nonlinear Systems, Macmillan Publishing, New York, 1992.
7. Vannelli, A. and M. Vidyasagar, 'Maximal Lyapunov functions and domains of attraction for autonomous nonlinear systems', Automatica, 21, 69-80 (1985).
8. Walker, J. A. and N. H. McClamroch, 'Finite regions of attraction for the problem Luré', Int. J. Control, 6, 331-336 (1967).
9. Weissenberger, S., 'Application of results from the absolute stability problem to the computation of finite stability domains', IEEE Trans. Automat. Control, AC-13, 124-125 (1968).
10. Willems, J. L., The computation of finite stability regions by means of open Lyapunov surfaces', Int. J. Control, 10, 537-544 (1969).
11. Haddad, W. M. and D. S. Bernstein, 'Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle and Popov theorems and their application to robust stability, part I: Continuous-time theory', Int. J. Robust and Nonlinear Control, 3, 313-339 (1993).
12. Vidyasagar, M., Nonlinear Systems Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1993.
13. Willems, J. L., Optimum Lyapunov functions and transient stability regions for multimachine power systems', Proc. Inst. Elect. Eng., 117, 573-577 (1970).
14. Willems, J. L. and J. C. Willems, The application of Lyapunov methods to the computation of transient stability regions for multimachine power systems', IEEE Trans. Power Apparatus and Systems, PAS-89, 795-801 (1970).
15. Haddad, W. M. and V. Kapila, 'Fixed-architecture controller synthesis for systems with input-output time-varying nonlinearities', Int. J. Robust and Nonlinear Control, to appear.
16. Tyan, F. and D. S. Bernstein, 'Anti-windup compensator synthesis for systems with saturating actuators', Int. J. Robust and Nonlinear Control, 5, 521-537 (1995).
17. Narendra, K. S. and J. H. Taylor, Frequency Domain Criteria for Absolute Stability, Academic Press, New York, 1973.
18. Gahinet, P. and A. Nemirovskii, LMI Lab: A Package for Manipulation and Solving LMI's INRIA, France, 1993.