Control of Fractional Periodic Discrete-Time Linear Systems by Partial Eigenvalue Assignment of State Feedback Matrices

Abstract

In this article to control of fractional-order periodic discrete-time linear system a special form of state feedback matrix is proposed to assign suitable eigenvalues to closed-loop monodromy matrix of the periodic discrete-time system. It makes large monodromy matrix and changing all of eigenvalues make some problems. By reassigning a part of bad spectrums of monodromy matrix, leaving the rest of the spectrums invariant, we have lower oredered matrix to modify the dynamic response of linear system and we can lie the poles of this systems in the unit circle by less expenses. Controlling the alternating states by other controllers such that the controllability of the resulting system is preserved. The effectiveness of our algorithm is illustrated by an example.