×

Stabilization of globally asymptotically controllable systems. (Stabilisation des systèmes globalement asymptotiquement commandables.) (French. Abridged English version) Zbl 0952.93113

The author illustrates here in abridged form some new results concerning control systems of the general form \(\dot x= f(x,u)\).
1. If the system is globally asymptotically controllable, then it admits a control Lyapunov function which is semi-concave (and, hence, locally Lipschitz continuous) for \(x\neq 0\).
2. As a consequence, if the system is globally asymptotically controllable it is possible to construct a discontinuous stabilizing feedback (provided that solutions are intended in Euler sense).
3. If the system is affine and globally asymptotically controllable, and the solutions are intended in Carathéodory sense, there exists a stabilizing feedback which is continuous on an open dense set.

MSC:

93D15 Stabilization of systems by feedback
93D30 Lyapunov and storage functions
PDF BibTeX XML Cite
Full Text: DOI