Non-quadratic Lyapunov functions for performance analysis of saturated systems

Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

Volumn 2005, Issue , 2005, Pages 8106-8111

  Hu, Tingshu ^b   Teel, Andrew R ^a   Zaccarian, Luca ^c  

^a University of California   (United States)

^b Umass Lowell ^*  (United States)

^c UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

Deadzone; Domain of attraction; Lyapunov functions; Nonlinear 2 gain; Reachable set; Saturation

Indexed keywords

LYAPUNOV METHODS; MATRIX ALGEBRA; NUMERICAL METHODS; SYSTEM STABILITY;

LYAPUNOV FUNCTIONS; MAX QUADRATIC FUNCTION; REACHABLE SET;

CONTROL SYSTEM ANALYSIS;

EID: 33847231911     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2005.1583474     Document Type: Conference Paper

References (20)

1. F. Blanchini. Nonquadratic lyapunov functions for robust control. Automatica, 31:451-461, 1995.
2. R. K. Brayton and C. H. Tong. Stability of dynamical systems: a constructive approach. IEEE Trans. on Circuits and Systems, 26:224-234, 1979.
3. G. Chesi, A. Garulli, A. Tesi, and A. Vicino. Homogeneous lyapunov functions for systems with structured uncertainties. Automatica, 39:1027-1035, 2003.
4. F.H. Clarke. Optimization and Nonsmooth Analysis. Society for Industrial an Applied Mathematics, 1990.
5. W.P. Dayawansa and C.F. Martin. A converse Lyapunov theorem for a class of dynamical systems with undergo switching. IEEE Trans. Aut. Cont., 44(4):751-759, April 1999.
6. R. Goebel, T. Hu, and A. R. Teel. Dual matrix inequalities in stability and performance analysis of linear differential/difference inclusions. In L. Menini, L. Zaccarian, and C. Abdallah, editors, Current Trends in Nonlinear Systems and Control. Birkhauser, to appear, 2005.
7. R. Goebel, A. R. Teel, T. Hu, and Z. Lin. A collection of robust control problems leading to LMI's. In IEEE Conference on Decision and Control, 2004.
8. A. Hassibi, J. How, and S. Boyd. A path-following method for solving bmi problems in control. In American Control Conference, pages 1385-1389, 1999.
9. T. Hu and Z. Lin. Composite quadratic lyapunov functions for constrained control systems. IEEE Transactions on Automatic Control, 48(3):440-450, 2003.
10. T. Hu and Z. Lin. Properties of convex hull quadratic lyapunov functions. IEEE Transactions on Automatic Control, 49(7): 1162-1167, 2004.
11. T. Hu, Z. Lin, and B.M. Chen. An analysis and design method for linear systems subject to actuator saturation and disturbance. Automatica, 38(2):351-359, 2002.
12. T. Hu, Z. Lin, R. Goebel, and A. R. Teel. Stability regions for saturated linear systems via conjugate lyapunov functions. In IEEE Conf. on Dec. and Contr, 2004.
13. 2 gain and regional analysis for linear systems with anti-windup compensation. In American Control Conference, pages 3391-3396, Portland (OR), USA, June 2005.
14. T. Hu, A.R. Teel, and L. Zaccarian. Performance analysis of saturated systems via two forms of differential inclusions. In Joint CDC-ECC, Seville, Spain, December 2005.
15. Z. Jarvis-Wloszek and A. K. Packard. An LMI method to demonstrate simultaneous stability using non-quadratic polynomial lyapunov functions. In IEEE Conf. on Decision and Control, pages 287-292, Las Vegas, 2002.
16. M. Johansson and A. Rantzer. Computation of piecewise quadratic lyapunov functions for hybrid systems. IEEE Trans. Aut. Com., 43(4):555-559, April 1998.
17. A. P. Molchanov. Criteria of asymptotic stability of differential and difference inclusions encountered in control theory. Systems & Control Letten, 13:59-64, 1989.
18. E.F. Mulder and M.V. Kothare. Synthesis of stabilizing anti-windup controllers using piecewise quadratic Lyapunov functions. In Proceedings of the American Control Conference, pages 3239-3243, Chicago (IL), June 2000.
19. E.F. Mulder, M.V. Kothare, and M. Morari. Multivariable anti-windup controller synthesis using linear matrix inequalities. Automatica, 37(9): 1407-1416, September 2001.
20. L. Xie, S. Shishkin, and M. Fu. Piecewise lyapunov functions for robust stability of linear time-varying systems. Systems & Control Letters, 31:165-171, 1997.