Discretizing LTI Descriptor (Regular) Differential Input Systems with Consistent Initial Conditions

Athanasios D Karageorgos,Athanasios A Pantelous,Grigoris I Kalogeropoulos

doi:10.1155/2010/810605

Abstract

A technique for discretizing efficiently the solution of a Linear descriptor (regular) differential input system with consistent initial conditions, and Time-Invariant coefficients (LTI) is introduced and fully discussed. Additionally, an upper bound for the error ‖x¯(kT)−x¯k‖ that derives from the procedure of discretization is also provided. Practically speaking, we are interested in such kind of systems, since they are inherent in many physical, economical and engineering phenomena.

Highlights

Preliminary ResultsDuring the discretization or sampling process, we should replace the original continuoustime systems with finite sequences of values at specified discrete-time points
The discretization or sampling process is occurred whenever significant measurements for the system are obtained in an intermittent fashion
The Weierstrass canonical form of the regular pencil sE − A is defined by sEw − Aw block diag sIp − Jp, sHq − Iq, 1.2 where the first normal Jordan type block sIp − Jp is uniquely defined by the set of f.e.d

Summary

Preliminary Results

During the discretization or sampling process, we should replace the original continuoustime systems with finite sequences of values at specified discrete-time points. I First, we want to provide a computationally efficient method for discretizing LTI descriptor regular differential systems with input signals and consistent initial conditions. Some basic concepts and definitions from matrix pencil theory are introduced; see for more details 2–4, 17–22 et al the class of strict equivalence is characterized by a uniquely defined element, known as a WCF, that is, sEw − Aw. when the pencil sE − A is regular, we have elementary divisors of the following type:. ; iii e.d. of the type sq are called infinite elementary divisors i.e.d. the Weierstrass canonical form of the regular pencil sE − A is defined by sEw − Aw block diag sIp − Jp, sHq − Iq , 1.2 where the first normal Jordan type block sIp − Jp is uniquely defined by the set of f.e.d. ν s − a1 p1 , . Hqi Bq,lu i to , with Cp ∈ M p × 1, C

Discretisation of Nonhomogeneous LTI Descriptor Regular Differential System

Conclusion