The exponential decay of transient values in discrete-time nonlinear standard and fractional orders systems with linear positive linear part and positive feedbacks is investigated. Sufficient conditions for the exponential decay of transient values in this class of positive nonlinear systems are established. A procedure for computation of gains characterizing the class of nonlinear elements are given and illustrated on simple example.

The asymptotic stability of fractional positive descriptor continuous-time and discretetime linear systems is considered. New sufficient conditions for stability of fractional positive descriptor linear systems are established. The efficiency of the new stability conditions are demonstrated on numerical examples of fractional continuous-time and discrete-time linear systems.

The Floquet-Lyapunov transformation is extended to fractional discrete-time linear systems with periodic parameters. A procedure for computation of the transformation is proposed and illustrated by a numerical example.