Outer invariance entropy for discrete-time linear systems on Lie groups

We introduce discrete-time linear control systems on connected Lie groups and present an upper bound for the outer invariance entropy of admissible pairs (K,Q). If the stable subgroup of the uncontrolled system is closed and K has positive measure for a left invariant Haar measure, the upper bound coincides with the outer invariance entropy.

Metric invariance entropy and conditionally invariant measures

Two notions of metric invariance entropy are constructed with respect to conditionally invariant measures for control systems in discrete time and it is shown that they are invariant under conjugacies.