On Stability of Totally Controlled Systems

A. Ya. Narmanov

Matematičeskie trudy, Tome 4 (2001) no. 1, pp. 94-110.

Résumé

It is known that a smooth control system whose phase space is a smooth manifold $M$ generates some smooth foliation with singularities. This foliation has the property that, for every point $\eta\in M$, the controllability set with goal point $\eta$ is a subset of the leaf passing through $\eta$. In the first part of the article, we obtain sufficient conditions under which a system totally controlled on a fixed leaf is totally controlled on the leaves close to this leaf. In the second part, we consider a control system with a parameter totally controlled for some value of the parameter. We obtain sufficient conditions under which the system is totally controlled for the values of the parameter close to a given value.

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