Input to state stabilizing controller for systems with coarse quantization

Yoav Sharon, Daniel Liberzon

Research output: Contribution to journalArticlepeer-review


We consider the problem of achieving input-to-state stability (ISS) with respect to external disturbances for control systems with quantized measurements. Quantizers considered in this paper take finitely many values and have an adjustable center and zoom parameters. Both the full state feedback and the output feedback cases are considered. Similarly to previous techniques from the literature, our proposed controller switches repeatedly between "zooming out" and "zooming in". However, here we use two modes to implement the "zooming in" phases, which allows us to attenuate an unknown disturbance while using the minimal number of quantization regions. Our analysis is trajectory-based and utilizes a cascade structure of the closed-loop hybrid system. We further show that our method is robust to modeling errors using a specially adapted small-gain theorem. The main results are developed for linear systems, but we also discuss their extension to nonlinear systems under appropriate assumptions.

Original languageEnglish (US)
Article number6003764
Pages (from-to)830-844
Number of pages15
JournalIEEE Transactions on Automatic Control
Issue number4
StatePublished - Apr 2012


  • Disturbances
  • input-to-state stability (ISS)
  • quantized systems
  • stability of hybrid systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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