Stability of linear discrete systems with variable delays

Abstract

The paper studies the stability of linear systems of difference equations with single delay x(k+1)=A(k)+∑s=1lBs(k)x(k−ms(k)), k=0, 1, … where l ≥ 1, A is a constant n × n matrix, Bs(k) are n × n matrices, ms(k) ∈ ℕ ∪ {0} and ms ≤ m for an m ∈ ℕ. Sufficient conditions for the stability are derived using the method of Lyapunov functions.