Simple criteria for stability and instability of discrete dynamic systems

The stability problems of interval matrices and a class of discrete dynamic systems are investigated by means of the analysis technique of matric eigenvalues. 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 matrices. That the conditions of lower (upper) boundary matrix being nonnegtive (nonpositive) in the previous literatures are abandoned. The proposed results are wider applicable and less conservative than existing criteria, and some of them are inclusive of the previous results of stability.