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This paper studies left invertibility of discrete-time linearoutput-quantized systems. Quantized outputs are generated according to a givenpartition of the state-space, while inputs are sequences on a finite alphabet.Left invertibility, i.e. injectivity of I/O map, is reduced to leftD-invertibility, under suitable conditions. While left invertibility takes intoaccount membership to sets of a given partition, left D-invertibility considersonly membership to a single set, and is much easier to detect. The conditionunder which left invertibility and left D-invertibility are equivalent is thatthe elements of the dynamic matrix of the system form an algebraicallyindependent set. Our main result is a method to compute left D-invertibilityfor all linear systems with no eigenvalue of modulus one. Therefore we are ableto check left invertibility of output-quantized linear systems for a fullmeasure set of matrices. Some examples are presented to show the application ofthe proposed method.

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