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.
|Autori:||Dubbini, N.; Piccoli, B.; Bicchi, A|
|Titolo:||Left invertibility of discrete-time output-quantized systems: the linear case with finite inputs|
|Anno del prodotto:||2011|
|Digital Object Identifier (DOI):||10.1007/s00498-011-0063-x|
|Appare nelle tipologie:||1.1 Articolo in rivista|