Left invertibility of discrete-time output-quantized systems: the linear case with finite inputs
Abstract
This paper studies left invertibility of discrete-time linear output-quantized systems. Quantized outputs are generated according to a given partition of the state-space, while inputs are sequences on a finite alphabet. Left invertibility, i.e. injectivity of I/O map, is reduced to left D-invertibility, under suitable conditions. While left invertibility takes into account membership to sets of a given partition, left D-invertibility considers only membership to a single set, and is much easier to detect. The condition under which left invertibility and left D-invertibility are equivalent is that the elements of the dynamic matrix of the system form an algebraically independent set. Our main result is a method to compute left D-invertibility for all linear systems with no eigenvalue of modulus one. Therefore we are able to check left invertibility of output-quantized linear systems for a full measure set of matrices. Some examples are presented to show the application of the proposed method.
Keywords
Cite
@article{arxiv.1103.4039,
title = {Left invertibility of discrete-time output-quantized systems: the linear case with finite inputs},
author = {Nevio Dubbini and Benedetto Piccoli and Antonio Bicchi},
journal= {arXiv preprint arXiv:1103.4039},
year = {2011}
}