The Stability Cone for a Matrix Delay Difference Equation

Parameters of linear systems are subject to time changes. That is why in order to construct such systems it is desirable to know if they are not only stable but also able to estimate the distance of the system from the boundary of the stability region in the parameter space. Therefore, it makes sense to investigate the geometry of the subset of stable polynomials in the space of characteristic polynomials of linear systems in the canonical space 1 . This idea has already been applied to the investigation of geometry of the subset of stable polynomials in a two-dimensional subspace of the canonical space 2, 3 , the stability simplex for general difference equations 4 , connections of the convexity of the coefficients sequence with stability of difference equations 5 , and stability ovals for matrix difference equations of the form xn xn−1 Bxn−k with the delay k 6 . Consider the matrix equation