Stability of digitally interconnected linear systems

Taylor T. Johnson, Sayan Mitra, Cedric Langbort

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

Abstract

A sufficient condition for stability of linear subsystems interconnected by digitized signals is presented. There is a digitizer for each linear subsystem that periodically samples an input signal and produces an output that is quantized and saturated. The output of the digitizer is then fed as an input (in the usual sense) to the linear subsystem. Due to digitization, each subsystem behaves as a switched affine system, where state-dependent switches are induced by the digitizer. For each quantization region, a storage function is computed for each subsystem by solving appropriate linear matrix inequalities (LMIs), and the sum of these storage functions is a Lyapunov function for the interconnected system. Finally, using a condition on the sampling period, we specify a subset of the unsaturated state space from which all executions of the interconnected system reach a neighborhood of the quantization region containing the origin. The sampling period proves to be pivotal-if it is too small, then a dwell-time argument cannot be used to establish convergence, while if it is too large, an unstable subsystem may not receive timely-enough inputs to avoid diverging.

Original languageEnglish (US)
Title of host publication2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Pages2687-2692
Number of pages6
DOIs
StatePublished - Dec 1 2011
Event2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States
Duration: Dec 12 2011Dec 15 2011

Publication series

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

Other

Other2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
CountryUnited States
CityOrlando, FL
Period12/12/1112/15/11

ASJC Scopus subject areas

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

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  • Cite this

    Johnson, T. T., Mitra, S., & Langbort, C. (2011). Stability of digitally interconnected linear systems. In 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 (pp. 2687-2692). [6161264] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2011.6161264