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

Dubbini, Nevio and Piccoli, Benedetto and Bicchi, Antonio (2010) Left invertibility of discrete-time output-quantized systems: the linear case with finite inputs. Mathematics of Control, Signals, and Systems . ISSN 0932-4194 (Submitted)

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    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.

    Item Type: Article
    Additional Information: Articolo sottomesso e non ancora pubblicato.
    Uncontrolled Keywords: Left invertibility, uniform quantization, finite inputs, algebraic independent set, discrete time
    Subjects: Area01 - Scienze matematiche e informatiche > MAT/02 - Algebra
    Divisions: Dipartimenti (until 2012) > DIPARTIMENTO DI MATEMATICA "L. TONELLI"
    Depositing User: Ph.D. Nevio Dubbini
    Date Deposited: 13 Sep 2010
    Last Modified: 20 Dec 2010 11:45
    URI: http://eprints.adm.unipi.it/id/eprint/737

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