Mathematics – Dynamical Systems
Scientific paper
2009-11-04
Mathematics
Dynamical Systems
2 figures
Scientific paper
This paper studies left invertibility of discrete-time linear I/O quantized linear systems of dimension 1. 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 in sets of a given partition, left D-invertibility considers only distances, and is very easy to detect. Considering the system $x^+=ax+u$, our main result states that left invertibility and left D-invertibility are equivalent, for all but a (computable) set of $a$'s, discrete except for the possible presence of two accumulation point. In other words, from a practical point of view left invertibility and left D--invertibility are equivalent except for a finite number of cases. The proof of this equivalence involves some number theoretic techniques that have revealed a mathematical problem important in itself. Finally, some examples are presented to show the application of the proposed method.
Bicchi Antonio
Dubbini Nevio
Monge Maurizio
No associations
LandOfFree
Left invertibility of I/O quantized linear systems in dimension 1: a number theoretic approach does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Left invertibility of I/O quantized linear systems in dimension 1: a number theoretic approach, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Left invertibility of I/O quantized linear systems in dimension 1: a number theoretic approach will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-619708