Solving Linear Descriptor (Regular) Discrete-Time Delay System with (Non)-Consistent Initial Conditions

A.D. Karageorgos (Greece), A.A. Pantelous (Greece, UK), and G.I. Kalogeropoulos (Greece)


Linear Descriptor (Regular) Delay Discrete-time Systems,Consistent and Non-consistent Initial Conditions, z-Transformation.


In this paper, a more general class of linear delay discrete time systems known in the literature as linear regular descriptor, discrete-time systems with delays and constant square matrix coefficients is being considered. These kinds of systems have appeared in many modeling processes; see for instance digital filters, growth population phenomena, financial and actuarial claims procedures etc. Using the complex Weierstrass canonical form of the associated matrix pencil the state equation is decomposed into two subsystems whose solutions are obtained. More over, the form of the initial function is given, so the corresponding initial value problem is uniquely solvable.

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