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Quantized Stabilization of Two-Input Linear Systems: A Lower Bound on the Minimal Quantization Density

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Book cover Hybrid Systems: Computation and Control (HSCC 2002)

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Abstract

In this paper we derive a lower bound on the density of the coarsest quantizer that quadratically stabilizes a two-input linear discrete time system. This result describes how much improvement could be expected in terms of reduced quantization density by using two inputs instead of one to quadratically stabilize the system. A by-product result is that the optimal quantizer is radially logarithmic. This is a generalization of the logarithmic quantizer obtained in previous work.

This research has been supported by NSF under the Career Award grant number ECS-0093950

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References

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Author information

Authors and Affiliations

  1. Dept. of Electrical and Computer Engineering, Iowa Sate University, USA

    Nicola Elia

  2. Dept. of Aeronautical and Astronautical Engineering, University of Illinois at Urbana-Champaign, USA

    Emilio Frazzoli

Authors
  1. Nicola Elia
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  2. Emilio Frazzoli
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Editor information

Editors and Affiliations

  1. Department of Aeronautics and Astronautics, Stanford University, 250 Durand Building MC4035, 94305-4035, Stanford, CA, USA

    Claire J. Tomlin

  2. Department of Computer Science, University of British Columbia, 201-2366 Main Mall, V6T1Z4, Vancouver BC, Canada

    Mark R. Greenstreet

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© 2002 Springer-Verlag Berlin Heidelberg

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Elia, N., Frazzoli, E. (2002). Quantized Stabilization of Two-Input Linear Systems: A Lower Bound on the Minimal Quantization Density. In: Tomlin, C.J., Greenstreet, M.R. (eds) Hybrid Systems: Computation and Control. HSCC 2002. Lecture Notes in Computer Science, vol 2289. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45873-5_16

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  • DOI: https://doi.org/10.1007/3-540-45873-5_16

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43321-7

  • Online ISBN: 978-3-540-45873-9

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