|
Some properties of Lyapunov function sets
Author(s):
Emmanuel
Moulay
Journal:
Proc. Amer. Math. Soc.
138
(2010),
4067-4073.
MSC (2010):
Primary 93D20, 34D20, 37B25;
Secondary 52A05
Posted:
June 18, 2010
Previous version:
Original version posted June 16, 2010
Corrected version:
Current version
corrects received dates.
MathSciNet review:
2679627
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
The purpose of this paper is to study some geometrical and topological properties of Lyapunov function sets. These functions are very useful in control theory to solve stability problems. We focus our attention on the set of Lyapunov functions associated with continuous and discontinuous nonlinear systems.
References:
-
- 1.
- J. P. Aubin and A. Cellina, Differential inclusions, vol. 264, Springer-Verlag, Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, Berlin, 1984. MR 755330 (85j:49010)
- 2.
- F. H. Clarke, Yu S. Ledyaev, and R. J. Stern, Asymptotic stability and smooth Lyapunov functions, J. Differential Equations 149 (1998), 69-114. MR 1643670 (99k:34109)
- 3.
- N. Cohen and I. Lewkowicz, Convex invertible cones and the Lyapunov equation, Linear Algebra Appl. 250 (1997), 105-131. MR 1420573 (98b:15022)
- 4.
- K. Deimling, Multivalued differential equations, De Gruyter Series in Nonlinear Analysis and Applications, 1, Walter de Gruyter, Berlin, 1992. MR 1189795 (94b:34026)
- 5.
- A. F. Filippov, Differential equations with discontinuous righthand sides, Kluwer Academic Publishers, Dordrecht-Boston-London, 1988. MR 1028776 (90i:34002)
- 6.
- W. Hahn, Stability of motion, Springer-Verlag, Berlin-Heidelberg-New York, 1967. MR 0223668 (36:6716)
- 7.
- J. Kurzweil, On the inversion of Lyapunov's second theorem on stability of motion, Amer. Math. Soc. Transl. (2) 24 (1963), 19-77.
- 8.
- T. J. Laffey and H. Šmigoc, Common solution to the Lyapunov equation for
 complex matrices, Linear Algebra Appl. 420 (2007), no. 2-3, 609-624. MR 2278236 (2007k:15020) - 9.
- Y. Li and X. Chen, Stability on multi-robot formation with dynamic interaction topologies, IEEE International Conference on Intelligent Robots and Systems (Alberta, Canada), 2005, pp. 1325-1330.
- 10.
- S.M. Madani-Esfahani, M. Hached, and S.H. Żak, Estimation of sliding mode domains of uncertain variable structure systems with bounded controllers, IEEE Trans. Automat. Control 35 (1990), no. 4, 446-449. MR 1047998
- 11.
- O. Mason and R. Shorten, The geometry of convex cones associated with the Lyapunov inequality and the common Lyapunov function problem, Electron. J. Linear Algebra 12 (2005), 42-63. MR 2139459 (2006k:37026)
- 12.
- A. N. Michel, N. R. Sarabudla, and R. K. Miller, Stability analysis of complex dynamical systems: Some computational methods, Circuits Systems Signal Process. 1 (1982), no. 2, 171-202. MR 736885 (85e:34051)
- 13.
- C. Zuily and H. Queffelec, Eléments d'analyse pour l'agrégation, Masson, Paris, 1996.
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2010):
93D20, 34D20, 37B25,
52A05
Retrieve articles in all Journals with
MSC (2010):
93D20, 34D20, 37B25,
52A05
Additional Information:
Emmanuel
Moulay
Affiliation:
Xlim (UMR-CNRS 6172), Département Signal Image Communications, Université de Poitiers, Bvd. Marie et Pierre Curie, B.P. 30179, 86962 Futuroscope Chasseneuil Cedex, France
Email:
emmanuel.moulay@univ-poitiers.fr
DOI:
10.1090/S0002-9939-2010-10298-8
PII:
S 0002-9939(2010)10298-8
Keywords:
Lyapunov functions,
convex cones
Received by editor(s):
January 1, 2001
Received by editor(s) in revised form:
June 22, 2001
Posted:
June 18, 2010
Additional Notes:
The author was supported in part by the CNRS
Communicated by:
Peter A. Clarkson
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
