Left invertibility of discrete-time output-quantized systems: the linear case with finite inputs

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 (so also left invertibility for a full measure matrix set) for all linear systems with no eigenvalue of modulus one. Some examples are presented to show the application of the proposed method. Left invertibility, uniform quantization, finite inpu...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Nevio Dubbini, Benedetto Piccoli, Antonio Bicchi
• Keywords: CORR 2011, Education, Invertibility, Linear Output-quantized Systems, Single Set