On the Existence of Solutions of Degenerate Discrete-Time Systems

Abstract

We consider a nonstationary linear discrete-time descriptor system with rectangular matrix coefficients defined on a finite horizon. An answer is obtained to the question as to what the largest number of unknown vectors that can be found from a given finite number of equations is. In a similar way, the solvability of nonstationary linear continuous- or discrete-time systems, as well as (in the local sense) nonlinear discrete-time systems, is studied. It is shown that in cases where the considered linear (or nonlinear) system retains its internal structure, it is possible to find its solutions on an infinite horizon. The proposed approach has sufficient generality and automatically solves the problem of consistency of the initial data.