On stability of linear time-varying infinite-dimensional discrete-time systems

Abstract

The asymptotic behaviour of linear time-varying infinite-dimensional discrete-lime systems is considered. The introduced notions are: weak power equistability, power equistability, uniform power equistability, l p -equistability, uniform / l p -equistability and l p(x) -equistability. It is shown that they are identical. A generalization of the concept of spectral radius of a single operator is also proposed. It is proven that any time-varying system is uniformly power equistable if and only if the generalized spectral radius of the sequence of the operators which define the system considered is less than one.