Exponential asymptotic stability of delay partial difference equations

This paper is concerned with the linear delay partial difference equation u(i,j+1)=a(i,j)u(i+1,j)+b(i,j)u(i,j)+p(i,j)u(i−σ,j−τ) where σ and τ are two nonnegative integers, a(i,j), b(i,j), p(i,j) are three real sequences defined on i ≥ 0, j ≥ 0. Some sufficient conditions for this equation to be exponentially asymptotically stable are derived.