Markov chains, entropy, and fundamental limitations in nonlinear stabilization

Prashant G. Mehta, Umesh Vaidya, Andrzej Banaszuk

Research output: Contribution to journalArticlepeer-review


In this paper, we propose a novel methodology for establishing fundamental limitations in nonlinear stabilization. To aid the analysis, we express the stabilization problem as control of Markov chains. Using Markov chains, we derive the limitations as certain maximum probability bounds or as positive conditional entropy of the certain signals in the feedback loop. The former is related to the infeasibility of the asymptotic stabilization in the presence of quantization and the latter to the Bode integral formula. In either cases, it is shown that uncertainty - associated here with the unstable eigenvalues of the linearization - leads to fundamental limitations.

Original languageEnglish (US)
Pages (from-to)784-791
Number of pages8
JournalIEEE Transactions on Automatic Control
Issue number3
StatePublished - Apr 2008


  • Ergodic theory
  • Fundamental limitations
  • Markov chains
  • Nonlinear systems
  • Stabilization

ASJC Scopus subject areas

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


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