Absolute stability with a generalized sector condition

IEEE Transactions on Automatic Control

Volumn 49, Issue 4, 2004, Pages 535-548

  Hu, Tingshu ^a   Huang, Bin ^a   Lin, Zongli ^a  

^a University of Virginia   (United States)

Author keywords

Absolute contractive invariance (ACI); Absolute stability; Concave function; Convex function; Generalized sector

Indexed keywords

FUNCTION EVALUATION; MATHEMATICAL MODELS; NONLINEAR CONTROL SYSTEMS; PIECEWISE LINEAR TECHNIQUES;

ABSOLUTE CONTRACTIVE INVARIANCE; ABSOLUTE STABILITY;

STABILITY CRITERIA;

EID: 2442430440     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2004.825657     Document Type: Article

References (32)

1. M. A. Aizerman and F. R. Gantmacher, Absolute Stability of Regulator Systems. San Francisco, CA: Holden-Day, 1964.
2. M. Arcak and A. Teel, "Input-to-state stability for a class of lurie systems," Automatica, vol. 38, pp. 1945-1949, 2002.
3. D. S. Bernstein and A. N. Michel, "A chronological bibliography on saturating actuators," Int. J. Robust Nonlin. Control, vol. 5, pp. 375-380. 1995.
4. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, ser. SIAM Studies in Applied Mathematics. Philadelphia: SIAM, 1994.
5. Y.-S. Chou, A. L. Tits, and V. Balakrishnan, "Stability multipliers and μ upper bounds: Connections and implications for numerical verification of frequency domain conditions," IEEE Trans. Automat. Contr., vol. 44, pp. 906-913, June 1999.
6. T. Chu, L. Huang, and L. Wang, "Absolute stability and guaranteed domain of attraction for MIMO discrete-time Lur'e systems," in Proc. 40th IEEE Conf. Decision Control, Orlando, FL, 2001, pp. 1711-1716.
7. E. J. Davison and E. M. Kurak, "A computational method for determining quadratic lyapunov functions for nonlinear systems," Automatica, vol. 7, pp. 627-636, 1971.
8. E. G. Gilbert and K. T. Tan, "Linear systems with state and control constraints: The theory and application of maximal output admissible sets," IEEE Trans. Automat. Contr., vol. 36, pp. 1008-1020, Sept. 1991.
9. K. Gu, "Absolute stability of systems under block diagonal memoryless uncertainties," Automatica, vol. 31, no. 4, pp. 581-584, 1995.
10. W. M. Haddad, V. Kapila, and V. S. Chellabonia, "Guaranteed domain of attraction for multivariable lur'e systems via open lyapunov surfaces," in Proc. 13th IFAC Wold Congr., San Francisco, CA, 1996, pp. 13-18.
11. H. Hindi and S. Boyd, "Analysis of linear systems with saturating using convex optimization," in Proc. 37th IEEE Conf. Decision Control, 1998, pp. 903-908.
12. J. C. Hsu and A. U. Meyer, Modern Control Principles and Applications. New York: McGraw-Hill, 1968.
13. T. Hu and Z. Lin, Control Systems with Actuator Saturation: Analysis and Design. Boston, MA: Birkhäuser, 2001.
14. ____ and Z. Lin, "Exact characterization of invariant ellipsoids for linear systems with saturating actuators," IEEE Trans. Automat. Contr., vol. 47, pp. 164-169, Jan. 2002.
15. ____ and Z. Lin, "Composite quadratic lyapunov functions for constrained control systems," IEEE Trans. Automat. Contr., vol. 48, pp. 440-450, Mar. 2003.
16. T. Hu, Z. Lin, and B. M. Chen, "An analysis and design method for linear systems subject to actuator saturation and disturbance," Automatica,vol. 38, no. 2, pp. 351-359, 2002.
17. T. Hu, Z. Lin, and L. Qiu, "Stabilization of exponentially unstable linear systems with saturating actuators," IEEE Trans. Automat. Contr.,vol. 46, pp. 973-979, June 2001.
18. H. Khalil, Nonlinear Systems. Upper Saddle River, NJ: Prentice-Hall, 1996.
19. T. Kiyama and T. Iwasaki, "On the use of multi-loop circle for saturating control synthesis," Syst. Control Lett., vol. 41, pp. 105-114, 2000.
20. D. Liu and A. N. Michel, Dynamical Systems With Saturation Nonlinearities. London, U.K.: Springer-Verlag, 1994, vol. 195, Lecture Notes in Control and Information Sciences.
21. D. Liu and A. Molchanov, "Criteria for robust absolute stability of time-varying nonlinear continuous-time systems," Automatica, vol. 38, pp. 627-637, 2002.
22. A. Molchanov and D. Liu, "Robust absolute stability of time-varying nonlinear discrete-time systems," IEEE Trans. Circuit Syst. I, vol. 49, pp. 1129-1137, Aug. 2002.
23. K. A. Loparo and G. L. Blankenship, "Estimating the domain of attraction of nonlinear feedback systems," IEEE Trans. Automat. Contr., vol. AC-23, pp. 602-607, Aug. 1978.
24. K. S. Narendra and J. Taylor, Frequency Domain Methods for Absolute Stability. New York: Academic, 1973.
25. A. Megretski and A. Rantzer, "System analysis via integral quadratic constraints," IEEE Trans. Automat. Contr., vol. 42, pp. 819-830, May 1997.
26. J-J. E. Slotine and W. Li, Applied Nonlinear Control. Upper Saddle River, NJ: Prentice-Hall, 1991.
27. M. M. Vidyasagar, Nonlinear Systems Analysis. Upper Saddle River, NJ: Prentice-Hall, 1993.
28. T. Wada, M. Ikeda, Y. Ohta, and D. D. Siljak, "Parametric absolute stability of lur'e systems," IEEE Trans. Automat. Contr., vol. 43, pp. 1649-1653, Nov. 1998.
29. J. A. Walker and N. H. McClamroch, "Finite regions of attraction for the problem of lur'e," Int. J. Control, vol. 6, no. 4, pp. 331-336, 1967.
30. S. Weissenberger, "Application of results from the absolute stability to the computation of finite stability domains," IEEE Trans. Automat. Contr., vol. AC-13, pp. 124-125, Jan. 1968.
31. J. L. Willems, "The computation of finite stability regions by means of open Lyapunov surfaces," Int. J. Control, vol. 10, no. 5, pp. 537-544, 1969.
32. V. A. Yakubovich, "Frequency conditions for the absolute stability of control systems with several nonlinear and linear nonstationary blocks," Automat. Rem. Control, vol. 28, pp. 857-880, 1967.