Several simple and practical algebraic criteria (including sufficient conditions, necessary conditions, and necessary and sufficient conditions), for the mixed stability, asymptotic (discretely) stability and instability of interval matrices and discrete dynamic systems, are obtained, which use only the entries of boundary matrix of the interval matri.

This article is mainly based on the systemof state-space model, on the basis of some recent literature, Using the techniqueof matrix eigenvalues boundary and matrix analytical methods to study the sta-bility, the instability and mixed stability of the discrete dynamic systems.