Abstarct: In this thesis stability of fractional-order periodic discrete-time linear systems is explained‎. ‎Fractional systems‎ ‎provide an excellent instrument to describe memory and hereditary properties of various materials and‎ ‎processes‎. ‎The advantages or the real objects of the fractional-order systems are that we have more‎ ‎degrees of freedom in the model and that a ‘memory’ is included in the model (fractional-order systems‎ ‎have an unlimited memory).To modify the dynamic response of linear system we should change the poles‎ ‎of state feedback matrices‎. ‎Control of periodic fractional linear discrete-time system isn't possible in original form‎. ‎But it can be changes to a periodic linear discrete-time with arbitrary delays in time and having practical stability conditions‎. ‎Because of arbitrarily of delays we can make the conditions similar to fractional system that provides an excellent instrument to describe memory and hereditary properties of processes‎. ‎We proposed a special‎ ‎form of state feedback matrix to assign suitable eigenvalues to closed-loop mon‎odromy matrix of system. But it makes large monodromy matrix and changing all of‎ ‎eigenvalues make some problems. Reassigning a part of bad spectrums‎, ‎leaving the rest of the spectrums‎ ‎invariant‎, ‎we have lower ordered matrix to modify the dynamic response of linear system and we can‎ ‎make non-linear parametric for this new lower-ordered matrix by less expenses and better stability conditions‎‎. ‎stabilization of fractional-order periodic discrete-time linear system by a complete non‎- ‎linear parametric approach for pole assignment with respect to stability and reachablity of system via‎ ‎state feedback is proposed‎. ‎Non-linear parametric feedback matrix make some freedoms in conditions‎ ‎such as minimum norm of feedback matrix‎. ‎Numerical examples illustrate the effectiveness of the proposed approaches‎.‎