Computation of a lower bound for the induced L2 norm of LPV systems

Tamás Peni, Peter Seiler

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

Abstract

Determining the induced L2 norm of a linear, parameter-varying (LPV) system is an integral part of many analysis and robust control design procedures. In general, this norm cannot be determined explicitly. Most prior work has focused on efficiently computing upper bounds for the induced L2 norm. This paper presents a complementary algorithm to compute lower bounds for this norm. The proposed approach is based on restricting the parameter trajectory to be a periodic signal. This restriction enables the use of recent results for exact calculation of the L2 norm for a periodic time varying system. The proposed lower bound algorithm has two benefits. First, the lower bound complements standard upper bound techniques. Specifically, a small gap between the bounds indicates that further computation, e.g. upper bounds with more complex Lyapunov functions, is unnecessary. Second, the lower bound algorithm returns a worst-case parameter trajectory for the LPV system that can be further analyzed to provide insight into the system performance. Numerical examples are provided to demonstrate the applicability of the proposed approach.

Original languageEnglish (US)
Title of host publicationACC 2015 - 2015 American Control Conference
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages114-118
Number of pages5
ISBN (Electronic)9781479986842
DOIs
StatePublished - Jul 28 2015
Event2015 American Control Conference, ACC 2015 - Chicago, United States
Duration: Jul 1 2015Jul 3 2015

Publication series

NameProceedings of the American Control Conference
Volume2015-July
ISSN (Print)0743-1619

Conference

Conference2015 American Control Conference, ACC 2015
CountryUnited States
CityChicago
Period7/1/157/3/15

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