Admissibility and state feedback control for discrete-time rectangular descriptor systems

This paper studies the admissibility and state feedback stabilising control problems of discrete-time rectangular descriptor systems (DRDSs) with system matrix pair $ (E, A)\in R^{m\times n} $ (E, A)∈Rm×n. We first present definitions and lemmas for the consistency of initial condition, generalised regularity and causality of DRDSs. Secondly, we establish the equivalence relations between the admissibility of RDSs and their corresponding square systems. Then we give the admissibility results of DRDSs in the case of $ m \ge n $ m≥n and $ m \lt n $ m