@article {DPB11, title = {Left invertibility of discrete-time output-quantized systems: the linear case with finite inputs}, journal = {Mathematics of Control, Signals, and Systems}, volume = {23}, number = {1 - 2}, year = {2011}, note = {

published online 8 Sept. 2011

}, month = {November, 16}, pages = {117 - 139}, abstract = {

This paper studies left invertibility of discrete-time linear outputquantized systems. Quantized outputs are generated according to a given partition of the state-space, while inputs are sequences on a nite 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 (so also left invertibility for a full measure matrix set) 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 matrices set. Some examples are presented to show the application of the proposed method.

}, keywords = {Robotics}, doi = {10.1007/s00498-011-0063-x}, author = {N. Dubbini and B. Piccoli and A. Bicchi} }