Finite gain stabilization with logarithmic quantization

Chun Zhang, Geir E. Dullerud

Research output: Chapter in Book/Report/Conference proceedingConference contribution


In this paper, we consider the finite-gain stabilization problem in the case where there is logarithmic quantization in the feedback loop; more specifically, we consider a scalar-input discrete-time linear time invariant (LTI) system in the presence of additive deterministic or stochastic external disturbances, with logarithmically quantized state measurements available. Assuming that finite ℓp gain from the input to the states is achievable when the feedback is not quantized (or in the stochastic case that the pth-moment is finite), we show that there exist feasible logarithmic quantizers such that these boundedness properties are preserved when the state feedback is quantized. The main contribution of this paper is to show that static memoryless logarithmic quantizer is sufficient for finite gain stabilization. The quantizer density only depends on the open-loop system parameters. In addition to the controller construction, we also give explicit bounds on the ℓp gain, and in the stochastic case, the p th-moment of the state.

Original languageEnglish (US)
Title of host publicationProceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Print)1424414989, 9781424414987
StatePublished - 2007
Event46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States
Duration: Dec 12 2007Dec 14 2007

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Other46th IEEE Conference on Decision and Control 2007, CDC
Country/TerritoryUnited States
CityNew Orleans, LA

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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