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    Infimum Data Rates for Stabilising Markov Jump Linear Systems

    Nair, Girish N. and Dey, Subhrakanti and Evans, R.J. (2004) Infimum Data Rates for Stabilising Markov Jump Linear Systems. In: 42nd IEEE International Conference on Decision and Control. IEEE, pp. 1176-1181. ISBN 0780379241

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    In the past years, the problem of stabilising linear dynamical systems with low feedback data rates has been intensively investigated. A particular focus has been the characterisation of the infimum data rate for stabilisability, which specifies the smallest rate, in bits per unit time, at which information can circulate in a stable feedback loop. This paper extends this line of research to the case of fully-observed, finite-dimensional, linear systems without process noise but with control-independent, Markov parameters. Unlike previous formulations, the coding alphabet is permitted to be random and time-varying via a possible dependence on the observed Markov modes. Using quantisation techniques and real Jordan forms, it is shown that the smallest asymptotic mean data rate for stabilisability in r-th absolute output moment, over all coding and control schemes, is given by an exponent which measures the asymptotic mean growth rate of unstable eigenspace volumes. An explicit formula for it is obtained in the case of antistable dynamics. For scalar systems, this expression is quite different from an earlier one derived assuming a constant alphabet, in particular being independent of the moment order.

    Item Type: Book Section
    Additional Information: Cite as: G. N. Nair, S. Dey and R. J. Evans, "Infimum data rates for stabilising Markov jump linear systems," 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), 2003, pp. 1176-1181 Vol.2, doi: 10.1109/CDC.2003.1272767.
    Keywords: Infimum; data rates; stabilising; Markov; jump; linear systems;
    Academic Unit: Faculty of Science and Engineering > Electronic Engineering
    Faculty of Science and Engineering > Research Institutes > Hamilton Institute
    Item ID: 14452
    Identification Number:
    Depositing User: Subhrakanti Dey
    Date Deposited: 24 May 2021 16:08
    Publisher: IEEE
    Refereed: Yes
    Use Licence: This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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