Extremal storage functions and minimal realizations of discrete-time linear switching systems

Matthew Philippe, Ray Essick, Geir Dullerud, Raphael M. Jungers

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

Abstract

We study the p induced gain of discretetime linear switching systems with graph-constrained switching sequences. We first prove that, for stable systems in a minimal realization, for every p ≥ 1, the p-gain is exactly characterized through switching storage functions. These functions are shown to be the pth power of a norm. In order to consider general systems, we provide an algorithm for computing minimal realizations. These realizations are rectangular systems, with a state dimension that varies according to the mode of the system. We apply our tools to the study on the of p-gain. We provide algorithms for its approximation, and provide a converse result for the existence of quadratic switching storage functions. We finally illustrate the results with a physically motivated example.

Original languageEnglish (US)
Title of host publication2016 IEEE 55th Conference on Decision and Control, CDC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5533-5538
Number of pages6
ISBN (Electronic)9781509018376
DOIs
StatePublished - Dec 27 2016
Event55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States
Duration: Dec 12 2016Dec 14 2016

Publication series

Name2016 IEEE 55th Conference on Decision and Control, CDC 2016

Other

Other55th IEEE Conference on Decision and Control, CDC 2016
Country/TerritoryUnited States
CityLas Vegas
Period12/12/1612/14/16

ASJC Scopus subject areas

  • Artificial Intelligence
  • Decision Sciences (miscellaneous)
  • Control and Optimization

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