A brief remark on the topological entropy for linear switched systems

Abstract

In this brief note, we investigate the topological entropy for linear switched systems. Specifically, we use the Levi-Malcev decomposition of Lie-algebra to establish a connection between the basic properties of the topological entropy and the stability of switched linear systems. For such systems, we show that the topological entropy for the evolution operator corresponding to a semi-simple subalgebra is always bounded from above by the negative of the largest real part of the eigenvalue that corresponds to the evolution operator of a maximal solvable ideal part.