Stabilization of fractional order linear discrete-time control systems

The paper focuses on the stabilization of fractional order linear discrete-time systems with the Grunwald-Letnikov type fractional difference operator. The Z-transform, a highly effective method for stability analysis of linear control systems, is used to examine the behavior of the systems solutions. Given the crucial importance of stability in automatics, the primary concern is the stabilization of control systems. Stabilization involves determining the appropriate feedback that ensures the asymptotic stability of the system. In cases where the system is not initially asymptotically stable, stabilization is achieved through a state feedback. This feedback mechanism is derived from the eigenvalues of the matrix linked to the closed-loop system. The outlined asymptotic stability conditions offer guidance in eigenvalue placement to guarantee system stability.