Markov chains, entropy, and fundamental limitations in nonlinear stabilization

Prashant Girdharilal Mehta, Umesh Vaidya, Andrzej Banaszuk

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

Abstract

This paper is concerned with entropy based fundamental limitation results for the nonlinear stabilization of a scalar dynamical system. Using methods based on Ergodic theory, we pose the problem as control of Markov chains. It is shown that uncertainty, associated here with the unstable eigenvalue of the linearization, leads to fundamental limitations. These limitations arise as certain in-feasibility conditions for nonlinear stabilization in the presence of quantization or equivalently as positive conditional entropy of the output signal in the feedback loop. The former leads to a nonlinear stabilization result and latter to a fundamental limitation result.

Original languageEnglish (US)
Title of host publicationProceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
Pages5222-5227
Number of pages6
StatePublished - Dec 1 2006
Event45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States
Duration: Dec 13 2006Dec 15 2006

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other45th IEEE Conference on Decision and Control 2006, CDC
CountryUnited States
CitySan Diego, CA
Period12/13/0612/15/06

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ASJC Scopus subject areas

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

Cite this

Mehta, P. G., Vaidya, U., & Banaszuk, A. (2006). Markov chains, entropy, and fundamental limitations in nonlinear stabilization. In Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC (pp. 5222-5227). [4177813] (Proceedings of the IEEE Conference on Decision and Control).