Relations between nonlinear controllability and stabilizability. (Relations entre commandabilité et stabilisations non linéaires.) (French) Zbl 0813.93014

Coron, Jean-Michel

Brezis, H. (ed.) et al., Nonlinear partial differential equations and their applications. Collège de France Seminar, volume XI. Lectures presented at the weekly seminar on applied mathematics, Paris, France, 1989-1991. Harlow: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 299, 68-86 (1994).

The paper is devoted to the problem of globally and asymptotically stabilizing a controllable nonlinear system \(\dot x= f(x,y)\), with \(f\) a smooth function, by means of a smooth state feedback. A survey of the existing results is provided, in particular it is proved that in many cases, when sufficient conditions for the local controllability are satisfied, then a periodic dynamical state feedback law exists which asymptotically stabilizes the system. The possibility of stabilizing the system by means of discontinuous state feedback is also considered.
For the entire collection see [Zbl 0785.00024].

Reviewer: A.Perdon (Ancona)

MSC:

93B05	Controllability
93C10	Nonlinear systems in control theory
93D99	Stability of control systems

Keywords:

stabilizability of nonlinear systems; state feedback