Some Specific Properties of Positive Standard and Fractional Interval Systems

Abstract

AbstractSome specific properties of positive standard and fractional linear systems with interval state matrices are analyzed. The stability, positivity and transfer matrices of positive different orders fractional continuous-time linear systems are considered. New necessary and sufficient conditions for the asymptotic stability of positive different orders fractional linear systems are established. It is shown that the transfer matrices of positive asymptotically stable different orders fractional linear systems have only nonnegative coefficients. New conditions for the interval stability of positive standard and fractional linear systems are established. It is shown that the adjoint matrix of a singular Metzler matrix with zero sum of entries of each row (column) has all equal entries.