Predictor Feedback Control for Discrete-Time Systems With Input Delays and Multiple State Delays via Bivariant Fundamental Matrices

In this paper, the stabilization problem of discrete-time systems with both input delays and multiple state delays is concerned. For this end, two interesting properties are derived for the bivariant fundamental matrix related to a discrete-time linear system with multiple state delays. A prediction scheme of the considered system is presented via the corresponding bivariant fundamental matrix, and then a predictor-based feedback control law is proposed for the considered systems with both input delays and multiple state delays. Furthermore, the characteristic equation of the closed-loop system of the considered system under the designed predictor feedback law is analyzed. Finally, the effectiveness of the proposed method is illustrated by numerical examples.