Input-to-state stabilization of linear systems with quantized state measurements

Daniel Liberzon, Dragan Nešić

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 linear dynamics and quantized state measurements. Quantizers considered in this paper take finitely many values and have an adjustable "zoom"parameter. Building on an approach applied previously to systems with no disturbances, we develop a control methodology that counteracts an unknown disturbance by switching repeatedly between "zooming out" and "zooming in." Two specific control strategies that yield ISS are presented. The first one is implemented in continuous time and analyzed with the help of a Lyapunov function, similarly to earlier work. The second strategy incorporates time sampling, and its analysis is novel in that it is completely trajectory-based and utilizes a cascade structure of the closed-loop hybrid system. We discover that in the presence of disturbances, time-sampling implementation requires an additional modification which has not been considered in previous work.

Original languageEnglish (US)
Pages (from-to)767-781
Number of pages15
JournalIEEE Transactions on Automatic Control
Issue number5
StatePublished - May 2007


  • Disturbances
  • Hybrid control
  • Input-to-state stability (ISS)
  • Quantized feedback

ASJC Scopus subject areas

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


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