Stability of Discrete-Time Matrix Polynomials

Khanh Tu Ngo
Kelvin T. Erickson, Missouri University of Science and Technology

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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 x 1 vectors and the coefficients are m x m matrices. Stability of the system is related to the locations of the roots of the determinant of a real m x 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 infinity 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