On the Periodicity of Symbolic Observations of Piecewise Smooth Discrete-Time Systems

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Abstract

We study the behavior of discrete-time systems composed of a set of smooth transition maps coupled by a “quantized” feedback function. The feedback function partitions the state space into disjoint regions, and assigns a smooth transition function to each region. The main result is that under a constraint on the norm of the derivative of the transition maps, a bounded state trajectory with limit points in the interior of the switching regions leads to a region index sequence that is eventually periodic. Indeed, under these assumptions, we show that eventually the feedback function is determined by a finite state automaton. A similar result is proved in the case of finite state dynamic feedback.

Original languageEnglish (US)
Pages (from-to)807-813
Number of pages7
JournalIEEE Transactions on Automatic Control
Volume35
Issue number7
DOIs
StatePublished - Jan 1 1990

All Science Journal Classification (ASJC) codes

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

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