2011/03/21 by Nevio Dubbini, Dubbini, Nevio, Benedetto Piccoli +3
Engineering · #Advanced Control Systems Optimization #Control Systems and Identification #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1103.4039
openalex publication_date 2011/03/21 · openalex created_date 2022/09/29 · openalex updated_date 2026/07/28
This paper studies left invertibility of discrete-time linear\noutput-quantized systems. Quantized outputs are generated according to a given\npartition of the state-space, while inputs are sequences on a finite alphabet.\nLeft invertibility, i.e. injectivity of I/O map, is reduced to left\nD-invertibility, under suitable conditions. While left invertibility takes into\naccount membership to sets of a given partition, left D-invertibility considers\nonly membership to a single set, and is much easier to detect. The condition\nunder which left invertibility and left D-invertibility are equivalent is that\nthe elements of the dynamic matrix of the system form an algebraically\nindependent set. Our main result is a method to compute left D-invertibility\nfor all linear systems with no eigenvalue of modulus one. Therefore we are able\nto check left invertibility of output-quantized linear systems for a full\nmeasure set of matrices. Some examples are presented to show the application of\nthe proposed method.\n