Matrix rank based conditions for reachability/controllability of dicrete linear repetitive processes
type: Item
instance of: scholarly article
title: Matrix rank based conditions for reachability/controllability of dicrete linear repetitive processes
zbMATH Open document ID: 0933.93040
DOI: 10.1016/S0024-3795(97)10056-8
published in: Linear Algebra and its Applications
publication date: 2000-04-04T00:00:00Z
review text: Linear, finite-dimensional, time-invariant discrete repetitive control systems are considered. Using the so-called 2-D representation of the repetitive processes the general response formula is given in terms of the transition matrix of a suitably defined 2-D discrete system. Next, necessary and sufficient conditions for controllability and reachability in a given domain are formulated and proved. These conditions require verification of rank conditions for suitably defined controllability and reachability matrices. Moreover, several remarks and comments on the relationships between different concepts of controllability and observability are given. The relationships to the results which are known in the literature are also discussed. Similar controllability and reachability problems for multidimensional discrete control systems have been recently considered in the monograph [\textit{T. Kaczorek}, Linear control systems. Vol. 1: Analysis of multivariable systems. New York: John Wiley \& Sons Inc. (1992; Zbl 0784.93002); Vol. 2: Synthesis of multivariable systems and multidimensional systems. New York: John Wiley \& Sons Inc. (1993; Zbl 0784.93003)].
Mathematics Subject Classification ID: 93B55
zbMATH DE Number: 1354711
zbMATH Keywords: linear systems
zbMATH Keywords: discrete repetitive control systems
zbMATH Keywords: 2-D representation
zbMATH Keywords: reachability
zbMATH Keywords: controllability
author: Krzysztof Gałkowski
author: Eric Rogers
author: David H. Owens
reviewed by: Jerzy Klamka
MaRDI profile type: Publication
cites work: Iterative learning control using optimal feedback and feedforward actions
cites work: Stability analysis for linear repetitive processes
cites work: A discrete state-space model for linear image processing
cites work: Doubly-indexed dynamical systems: State-space models and structural properties
cites work: Stability of discrete non-unit memory linear repetitive processes—a two-dimensional systems interpretation
cites work: Q3138770
cites work: A review of 2-D implicit systems
cites work: New 2D models and a transition matrix for discrete linear repetitive processes
cites work: When does the local controllability of the general model of 2-D linear systems imply its local reachability?
cites work: Straight line reachability of Roesser model
cites work: State models and stability for 2-D filters
cites work: A new state-space model for linear discrete multipass processes
description: scientific article; zbMATH DE number 1354711