Limitations of nonlinear stabilization over erasure channels

Umesh Vaidya, Nicola Elia

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

11 Scopus citations

Abstract

In this paper, we study the problem of control of nonlinear systems over an erasure channel. The stability and performance metric are adopted from the ergodic theory of random dynamical systems to study the almost sure and second moment stabilization problem. The main result of this paper proves that, while there are no limitations for the almost sure stabilization, fundamental limitations arise for the second moment stabilization. In particular, we provide a necessary condition for the second moment stabilization of multi-state single input nonlinear systems expressed in terms of the probability of erasure and positive Lyapunov exponents of the open loop unstable system. The dependence of the limitation result on the Lyapunov exponents highlights, for the first time, the important role played by the global non-equilibrium dynamics of the nonlinear systems in obtaining the performance limitation. This result generalizes the existing results for the stabilization of linear time invariant systems over erasure channels and differs from the existing Bode-like fundamental limitation results for nonlinear systems, which are expressed in terms of the eigenvalues of the linearization.

Original languageEnglish (US)
Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
Pages7551-7556
Number of pages6
DOIs
StatePublished - Dec 1 2010
Externally publishedYes
Event2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States
Duration: Dec 15 2010Dec 17 2010

Publication series

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

Other

Other2010 49th IEEE Conference on Decision and Control, CDC 2010
CountryUnited States
CityAtlanta, GA
Period12/15/1012/17/10

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