Extremal Storage Functions and Minimal Realizations of Discrete-Time Linear Switching Systems

Philippe, Matthew;Jungers, Raphaël;Essick, Raymond;Dullerud, Geir
(2016) 2016 IEEE 55th Conference on Decision and Control (CDC) — Location: Las Vegas, USA (12.December.2016)

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  • Philippe, MatthewUCLouvain
    Author
  • Jungers, RaphaëlUCLouvain
    Collaborator
  • Essick, Raymond
    Collaborator
  • Dullerud, Geir
    Collaborator
Abstract
We study the Lp induced gain of discrete-time linear switching systems with graph-constrained switching sequences. We first prove that, for stable systems in a minimal realization, for every p≥1,the Lp 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 L2-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.
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Philippe, M. (2016). Extremal Storage Functions and Minimal Realizations of Discrete-Time Linear Switching Systems. Decision and Control (CDC. Published. 2016 IEEE 55th Conference on Decision and Control (CDC), Las Vegas, USA. https://doi.org/10.1109/CDC.2016.7799119 (Original work published 2016)