232 research outputs found
Invariance entropy, quasi-stationary measures and control sets
For control systems in discrete time, this paper discusses measure-theoretic
invariance entropy for a subset Q of the state space with respect to a
quasi-stationary measure obtained by endowing the control range with a
probability measure. The main results show that this entropy is invariant under
measurable transformations and that it is already determined by certain subsets
of Q which are characterized by controllability properties.Comment: 30 page
Growth rates for persistently excited linear systems
We consider a family of linear control systems where
belongs to a given class of persistently exciting signals. We seek
maximal -uniform stabilisation and destabilisation by means of linear
feedbacks . We extend previous results obtained for bidimensional
single-input linear control systems to the general case as follows: if the pair
verifies a certain Lie bracket generating condition, then the maximal
rate of convergence of is equal to the maximal rate of divergence of
. We also provide more precise results in the general single-input
case, where the above result is obtained under the sole assumption of
controllability of the pair
Bounds for Invariance Pressure
This paper provides an upper for the invariance pressure of control sets with
nonempty interior and a lower bound for sets with finite volume. In the special
case of the control set of a hyperbolic linear control system in R^{d} this
yields an explicit formula. Further applications to linear control systems on
Lie groups and to inner control sets are discussed.Comment: 16 page
Chain recurrence and Selgrade`s theorem for affine flows
Affine flows on vector bundles with chain transitive base flow are lifted to
linear flows and the decomposition into exponentially separated subbundles
provided by Selgrade's theorem is determined. The results are illustrated by an
application to affine control systems with bounded control range.Comment: 34 pages, 1 figur
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