Stabilization of nonlinear systems by use of semidefinite Lyapunov functions

Applied Mathematics Letters

Volumn 12, Issue 7, 1999, Pages 11-17

  Bensoubaya, M ^a   Ferfera, A ^a   Iggidr, A ^a  

^a INRIA   (France)

Author keywords

Feedback; Lyapunov functions; Nonlinear systems; Semidefinite functions; Stabilization

Indexed keywords

EID: 0001797118     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(99)00095-6     Document Type: Article

References (15)

1. A. Bacciotti, Local Stabiaization of Nonlinear Control systems, Series on Advances in Mathematics for Applied Sciences, World Scientific, Singapore, (1992).
2. R. Sepulchre, M. Jankovic and P. Kokotivic, Constructive Nonlinear Control, Springer-Verlag, New York, (1997).
3. E.D. Sontag, Feedback stabilization of nonlinear systems, In Robust Control of Linear Systems and Nonlinear Control, (Edited by M.A. Kaashoek et al.), pp. 61-81, Boston, MA, (1990).
4. W. Hahn, Stability of Motion, Springer-Verlag, New York, (1967).
5. D. Aeyels, Local and global stabilizability for nonlinear systems, In Theory and Applications of Nonlinear Control Systems, (Edited by C.I. Byrnes, et al.), pp. 93-105, Elsevier, Amsterdam, (1986).
6. R.W. Brockett, Asymptotic stability and feedback stabilization, In Differential Geometric Control Theory, (Edited by R.W. Brockett et al.) pp. 181-191, Birkhäuser, Boston, MA, (1983).
7. J. Carr, Applications of Center Manifold Theory, Springer-Verlag, New York, (1981).
8. P. Seibert and R. Suyarez, Global stabilization of nonlinear cascade systems, Systems Contr. Lett. 14, 347-352, (1990).
9. E.D. Sontag, Further facts about input to state stabilization, IEEE Trans. Automat. Contr. 35, 473-477, (1990).
10. M. Vidyasagar, Decomposition techniques for large scale systems with nonadditive interactions: Stability and stabilizablity, IEE Trans. Automat. Contr. 25, 773-779, (1980).
11. A. Iggidr, B. Kalitine and R. Outbib, Semidefinite Lyapunov functions stability and stabilization, Math. Contr. Signals Syst. 9, 95-106, (1996).
12. J.P. Gauthier and G. Bornard, Stabilisation des systèmes non linéaires, In Outils et Modèles Mathématiques pour l'Automatique et la Théorie du Signal, Editions du CNRS, (1981).
13. V. Jurdjevic and J.P. Quinn, Controllability and stability, J. Diff. Equ. 28, 381-389, (1978).
14. R. Outbib and G. Salletr, Stabilizability of the angular velocity of a rigid body revisited, Systems Contr. Lett. 18, 93-98, (1992).
15. J. Tsinias, Sufficient Lyapunov-like conditions for stabilization, Math. Contr. Singals. Syst. 2, 343-357, (1989).