The Stability Cone for a Matrix Delay Difference Equation

الملخص EN

We construct a stability cone, which allows us to analyze the stability of the matrix delay difference equation xn=Axn−1+Bxn−k.

We assume that A and B are m×m simultaneously triangularizable matrices.

We construct m points in ℝ3 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.