@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 = {<p>published online 8 Sept. 2011</p>
},
	month = {November, 16},
	pages = {117 - 139},
	abstract = {<p>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.</p>
},
	keywords = {Robotics},
	doi = {10.1007/s00498-011-0063-x},
	author = {N. Dubbini and B. Piccoli and A. Bicchi}
}
