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 language | English (US) |
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Title of host publication | ACC 2015 - 2015 American Control Conference |
Publisher | Institute of Electrical and Electronics Engineers Inc. |
Pages | 114-118 |
Number of pages | 5 |
ISBN (Electronic) | 9781479986842 |
DOIs | |
State | Published - Jul 28 2015 |
Event | 2015 American Control Conference, ACC 2015 - Chicago, United States Duration: Jul 1 2015 → Jul 3 2015 |
Publication series
Name | Proceedings of the American Control Conference |
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Volume | 2015-July |
ISSN (Print) | 0743-1619 |
Conference
Conference | 2015 American Control Conference, ACC 2015 |
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Country/Territory | United States |
City | Chicago |
Period | 7/1/15 → 7/3/15 |
Bibliographical note
Publisher Copyright:© 2015 American Automatic Control Council.