Adriano Da Silva

Invariance entropy for random control systems

For continuous-time random control systems, this paper introduces invariance entropy for random pairs as a measure for the amount of information necessary to achieve invariance of random weakly invariant compact subsets of the state space. For linear random control systems with compact control range, the invariance entropy is given by the sum of the real parts of the unstable eigenvalues of the uncontrolled system if we assume ergodicity.

The dynamic of a Lie group endomorphism

Abstract For a given endomorphism φ on a connected Lie group G this paper studies several subgroups of G that are intrinsically connected with the dynamic behavior of φ.

Topological conjugacy of linear systems on Lie groups

In this paper we study a classification of linear systems on Lie groups with respect to the conjugacy of the corresponding flows. We also describe stability according to Lyapunov exponents.