Maurizio Monge

Left invertibility of output-quantized MISO linear systems

Abstract This paper studies left invertibility of single-output discrete-time quantized linear systems. Quantized outputs are generated according to a given partition of the state-space, while inputs are sequences on a finite alphabet. Left invertibility deals with the possibility of recovering unknown inputs from the only knowledge of the outputs. It is reduced, under suitable conditions, to left D-invertibility: 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 easily (and algorithmically) detectable. Our main result is a sufficient condition for the equivalence between left invertibility and left D-invertibility in MISO system. In unidimensional systems the equivalence is valid except at most a finite (and computable) number of cases. These results allows the effective detection of left invertibility by means of left D-invertibility, which is algorithmically detectable. An example with effective computations is presented to show the application of the proposed method.