Abstract
In this paper, we prove that the solution of the autonomous q-difference system DqYx=AYqx with the initial condition Y0=Y0 where A is a constant square complex matrix, Dq is the Jackson q-derivative and 0<q<1, is asymptotically stable if and only if ℜλ<0 for all λ∈σA where σA is the set of all eigenvalues of A (the spectrum of A). This results are exploited to provide the orthogonality property of the discrete q-Hermite matrix polynomials.