Exponential stability of linear discrete systems with delay

Abstract

The paper studies the exponential stability to a linear system of difference equations with delay x(k+1)=A(k)x(k)+B(k)x(k−m(k)), k=0,1,… where A(k), B(k) are square constant matrices, m(k) ∈ ℕ and m(k) ≤ m*, m* ∈ ℕ. New sufficient conditions for exponential stability are derived and illustrated by an example.