The Gelfand formula for linear parameter-varying and linear switching systems
Abstract
It is shown that the Gelfand formula holds for a large class offamilies of linear time-varying systems, encompassing in particularstandard formulations of linear parameter-varying and linearswitching systems. By this result, the uniform exponential growthrate may be approximated to arbitrary precision by the growth rateof periodic systems within the family. This result extendsclassical results in the area of linear inclusions. The basic toolin the proof is a recent construction of parameter dependentLyapunov functions for the family of linear time-varying systemsthat exactly characterize the exponential growth rate.
