Brief paper: Control under quantization, saturation and delay: An LMI approach

  • Authors:

  • Emilia Fridman;Michel Dambrine

  • Affiliations:

  • Department of Electrical Engineering-Systems, Tel-Aviv University, Tel-Aviv 69978, Israel;Univ Lille Nord de France, F-59000 Lille, France and UVHC, LAMIH, F-59313 Valenciennes, France and CNRS, UMR 8530, F-59313 Valenciennes, France

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2009

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Abstract

This paper studies quantized and delayed state-feedback control of linear systems with given constant bounds on the quantization error and on the time-varying delay. The quantizer is supposed to be saturated. We consider two types of quantizations: quantized control input and quantized state. The controller is designed with the following property: all the states of the closed-loop system starting from a neighborhood of the origin exponentially converge to some bounded region (both, in R^n and in some infinite-dimensional state space). Under suitable conditions the attractive region is inside the initial one. We propose decomposition of the quantization into a sum of a saturation and of a uniformly bounded (by the quantization error bound) disturbance. A Linear Matrix Inequalities (LMIs) approach via Lyapunov-Krasovskii method originating in the earlier work [Fridman, E., Dambrine, M., & Yeganefar, N. (2008). On input-to-state stability of systems with time-delay: A matrix inequalities approach. Automatica, 44, 2364-2369] is extended to the case of saturated quantizer and of quantized state and is based on the simplified and improved Lyapunov-Krasovskii technique.