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

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

doi:10.1109/CDC.2016.7799119

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 proceeding › Conference contribution

4 Scopus citations

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 language	English (US)
Title of host publication	2016 IEEE 55th Conference on Decision and Control, CDC 2016
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	5533-5538
Number of pages	6
ISBN (Electronic)	9781509018376
DOIs	https://doi.org/10.1109/CDC.2016.7799119
State	Published - Dec 27 2016
Externally published	Yes
Event	55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States Duration: Dec 12 2016 → Dec 14 2016

Publication series

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

Other

Other	55th IEEE Conference on Decision and Control, CDC 2016
Country/Territory	United States
City	Las Vegas
Period	12/12/16 → 12/14/16

Bibliographical note

Publisher Copyright:
© 2016 IEEE.

Publisher link

10.1109/CDC.2016.7799119

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Philippe, M., Essick, R., Dullerud, G., & Jungers, R. M. (2016). Extremal storage functions and minimal realizations of discrete-time linear switching systems. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016 (pp. 5533-5538). Article 7799119 (2016 IEEE 55th Conference on Decision and Control, CDC 2016). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2016.7799119

Extremal storage functions and minimal realizations of discrete-time linear switching systems. / Philippe, Matthew; Essick, Ray; Dullerud, Geir et al.
2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. p. 5533-5538 7799119 (2016 IEEE 55th Conference on Decision and Control, CDC 2016).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Philippe, M, Essick, R, Dullerud, G & Jungers, RM 2016, Extremal storage functions and minimal realizations of discrete-time linear switching systems. in 2016 IEEE 55th Conference on Decision and Control, CDC 2016., 7799119, 2016 IEEE 55th Conference on Decision and Control, CDC 2016, Institute of Electrical and Electronics Engineers Inc., pp. 5533-5538, 55th IEEE Conference on Decision and Control, CDC 2016, Las Vegas, United States, 12/12/16. https://doi.org/10.1109/CDC.2016.7799119

Philippe M, Essick R, Dullerud G, Jungers RM. Extremal storage functions and minimal realizations of discrete-time linear switching systems. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc. 2016. p. 5533-5538. 7799119. (2016 IEEE 55th Conference on Decision and Control, CDC 2016). doi: 10.1109/CDC.2016.7799119

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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.",

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AB - 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.

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

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