5,314 research outputs found
A Semigroup associated to a linear control system on a Lie group
Let us consider a linear control system \Sigma on a connected Lie group G. It
is known that the accessibility set A from the identity e is in general not a
semigroup. In this article we associate a new algebraic object S to \Sigma
which turns out to be a semigroup, allowing the use of the semigroup machinery
to approach \Sigma. In particular, we obtain some controllability results
Invariance Entropy of Hyperbolic Control Sets
In this paper, we improve the known estimates for the invariance entropy of a
nonlinear control system. For sets of complete approximate controllability we
derive an upper bound in terms of Lyapunov exponents and for uniformly
hyperbolic sets we obtain a similar lower bound. Both estimates can be applied
to hyperbolic chain control sets, and we prove that under mild assumptions they
can be merged into a formula
The chain control set of a linear control system
In this paper, we analyze the chain control sets of linear control systems on
connected Lie groups. Our main result shows that the compactness of the central
subgroup associated with the drift is a necessary and sufficient condition to
assure the uniqueness and compactness of the chain control set
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