Stabilization of linear multi-parameter fractional difference control systems

The problem of stabilization of a fractional order linear control system with the Grunwald-Letnikov h-difference operator is discussed. To this goal the Z-transform, which can be considered as an effective method for stability analysis of linear systems, is used. The main result gives the sufficient and necessary condition for the stabilization of the linear multi-parameter fractional difference control system by a linear state feedback. This condition is related with the position of the roots of the characteristic equation associated with the given system.