Properties of the composite quadratic Lyapunov functions

IEEE Transactions on Automatic Control

Volumn 49, Issue 7, 2004, Pages 1162-1167

  Hu, Tingshu ^a   Lin, Zongli ^a  

^a University of Virginia   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CONSTRAINT THEORY; CONTROL NONLINEARITIES; INVARIANCE; LAGRANGE MULTIPLIERS; LINEAR SYSTEMS; MATRIX ALGEBRA; OPTIMIZATION; PARTIAL DIFFERENTIAL EQUATIONS; SET THEORY; THEOREM PROVING; VECTORS;

CONVEX HULL; LINEAR MATRIX INEQUALITIES; QUADRATIC LYAPUNOV FUNCTION;

LYAPUNOV METHODS;

EID: 3843073156     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2004.831132     Document Type: Article

References (18)

1. F. Blanchini, "Set invariance in control - A survey," Automatica, vol. 35, pp. 1747-1767, 1999.
2. G. Ferrari-Trecate, F. A. Cuzzola, D. Mignone, and M. Morari, "Analysis of discrete-time piecewise affine and hybrid systems," Automatica, vol. 38, pp. 2139-2146, 2002.
3. R. Goebel, A. R. Teel, T. Hu, and Z. Lin, "Dissipativity for dual linear differential inclusions through conjugate storage functions," in IEEE Conf. Decision Control, 2004, submitted for publication.
4. J.-B. Hiriart-Urruty and C. Lemarèchal, Convex Analysis and Minimization Algorithms I. New York: Springer-Verlag, 1993.
5. 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.
6. T. Hu, B. Huang, and Z. Lin, "Absolute stability with generalized sector condition," IEEE Trans. Automat. Contr., vol. 49, pp. 535-548, Apr. 2004.
7. T. Hu and Z. Lin, Control Systems With Actuator Saturation. Boston, MA: Birkhäuser, 2001.
8. T. Hu and Z. Lin, "Composite quadratic Lyapunov functions for constrained control systems," IEEE Trans. Automat. Contr., vol. 48, pp. 440-450, Mar. 2003.
9. T. Hu, Z. Lin, R. Goebel, and A. R. Teel, "Stability regions for saturated linear systems via conjugate Lyapnov functions," in IEEE Conf. Decision Control, 2004, submitted for publication.
10. M. Johansson and A. Rantzer, "Computation of piecewise quadratic Lyapunov functions for hybrid systems," IEEE Trans. Automat. Contr., vol. 43, pp. 555-559, May 1998.
11. R. Lozano, B. Brogliato, and I. D. Landau, "Passitivity and global stabilization of cascaded nonlinear systems," IEEE Trans. Automat. Contr., vol. 37, pp. 1386-1388, Sept. 1992.
12. F. Mazenc, R. Sepulchre, and M. Jankovic, "Lyapunov functions for stable cascades and applications to global stabilization," IEEE Trans. Automat. Contr., vol. 44, pp. 1795-1800, Nov. 1999.
13. F. Mazenc, "Strict Lyapunov functions for time-varying systems," Automatica, vol. 39, pp. 349-353, 2003.
14. H. M. Moller and R. Tenberg, "Multivariate polynomial system solving using intersections of eigenspaces," J. Symb. Comput., vol. 32, pp. 513-531, 2001.
15. B. E. A. Milani, "Piecewise-affine Lyapunov functions for discrete-time linear systems with saturating controls," in Proc. Amer. Control Conf., 2001, pp. 4206-4211.
16. L. Praly, B. d'Andrea-Novel, and J.-M. Coron, "Lyapunov design of stabilizing controllers for cascaded systems," IEEE Trans. Automat. Contr., vol. 36, pp. 1177-1181, Oct. 1991.
17. E. D. Sontag, "Stability and stabilization: Discontinuities and the effect of disturbances," in Nonlinear Analysis, Differential Equations, and Control. Norwell, MA: Kluwer, 1999, pp. 551-598.
18. G. F. Wredenhagen and P. R. Belanger, "Piecewise-linear LQ control for systems with input constraints," Automatica, vol. 30, pp. 403-416, 1994.