Stability conditions for a class of time-varying discrete-time systems (Q1068046)

The equilibrium of \(x(k+1)=A(k)x(k)\), \(x(k)\in R^ n\), \(k\in J_+\) is asymptotically stable if \(\cap^{\infty}_{k=0}Int \{x| \Gamma (k)x\leq 0\}\) is nonempty or if \(\Gamma\) (k) is diagonally dominant for all \(k\in J_+\), where \(\Gamma\) (k) is an \(n\times n\) real matrix written in terms of A(k).