Stability of discrete-time matrix polynomials

This paper derives conditions for the stability of discrete-time systems that can be modeled by a vector difference equation, where the variables are m/spl times/1 vectors and the coefficients are m/spl times/m matrices. Stability of the system is related to the locations of the roots of the determinant of a real m/spl times/m matrix polynomial of nth order. In this case, sufficient conditions for the system to be stable are derived. The conditions are imposed on the /spl infin/-norm of two matrices constructed from the coefficient matrices and do not require the computation of the determinant polynomial. The conditions are the extensions of one of the Jury sufficient conditions for a scalar polynomial. An example is used to illustrate the application of the sufficient conditions.