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Input and Output Finite-Level Quantized Linear Control Systems: Stability Analysis and Quantizer Design

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Abstract

This paper investigates the local stability of input- and output-quantized discrete-time linear time-invariant systems considering static finite-level logarithmic quantizers. The sector bound approach together with a relaxed stability notion is applied to derive an LMI-based method to estimate a set of admissible initial states and its attractor in a neighborhood of the system origin assuming that an output feedback controller and the quantizers are given. In addition, the stability analysis method is tailored to design an input and an output static finite-level logarithmic quantizers when a set of admissible initial states and an upper bound on the volume of its attractor are known. Numerical examples are presented to demonstrate the proposed stability analysis and quantizer design methods.

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Notes

  1. The volume of an ellipsoid \({\mathcal {A}}=\{ \zeta \in {\mathbb {R}}^{n_\zeta } : \zeta ' P_\mathrm{a} \zeta \le 1, P_\mathrm{a} >0 \}\) is given by \(c/\sqrt{\det (P_\mathrm{a})}\), where \(c\) is a constant that depends on \(n_\zeta \) (see, e.g., Bernstein (2009)).

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Authors and Affiliations

  1. Department of Automation and Systems, Universidade Federal de Santa Catarina, PO Box 476, Florianopolis, SC, 88040-900, Brazil

    Rafael Maestrelli & Daniel Coutinho

  2. Department of Systems and Control, Laboratório Nacional de Computação Científica (LNCC/MCTI), Petropolis, RJ, 25651-075, Brazil

    Carlos E. de Souza

Authors
  1. Rafael Maestrelli
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  2. Daniel Coutinho
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  3. Carlos E. de Souza
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Correspondence to Rafael Maestrelli.

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Maestrelli, R., Coutinho, D. & de Souza, C.E. Input and Output Finite-Level Quantized Linear Control Systems: Stability Analysis and Quantizer Design. J Control Autom Electr Syst 26, 105–114 (2015). https://doi.org/10.1007/s40313-014-0163-1

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  • DOI: https://doi.org/10.1007/s40313-014-0163-1

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