The stability cone for a matrix delay difference equation (Q539410)

Summary: We construct a stability cone, which allows us to analyze the stability of the matrix delay difference equation \(x_n=Ax_{n-1}+Bx_{n-k}\). We assume that \(A\) and \(B\) are \(m\times m\) simultaneously triangularizable matrices. We construct \(m\) points in \(\mathbb R^3\) which are functions of eigenvalues of matrices \(A,B\) such that the equation is asymptotically stable if and only if all the points lie inside the stability cone.