Computation of lower bounds for the induced L2 norm of LPV systems

Tamas Peni, Peter J. Seiler

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Summary Determining the induced L2 norm of a linear parameter-varying (LPV) system is an integral part of many analysis and robust control design procedures. Most prior work has focused on efficiently computing upper bounds for the induced L2 norm. The conditions for upper bounds are typically based on scaled small-gain theorems with dynamic multipliers or dissipation inequalities with parameter-dependent Lyapunov functions. This paper presents a complementary algorithm to compute lower bounds for the induced L2 norm. The proposed approach computes a lower bound on the gain by 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 linear time varying system. The proposed lower bound algorithm also returns a worst-case parameter trajectory for the LPV system that can be further analyzed to provide insight into the system performance.

Original languageEnglish (US)
Pages (from-to)646-661
Number of pages16
JournalInternational Journal of Robust and Nonlinear Control
Issue number4
StatePublished - Mar 10 2016

Bibliographical note

Funding Information:
This work was supported by the NSF under Grant No. NSF-CMMI-1254129 entitled "CAREER: Probabilistic Tools for High Reliability Monitoring and Control of Wind Farms". Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the NSF. The authors greatly acknowledge the help of Henrik Sandberg for making the MATLAB code of the numerical example presented in [6] available for the purpose of this research. Also, the authors thank the anonymous reviewers for the valuable advices and comments, which have contributed to the improvement of the initial submission.

Publisher Copyright:
Copyright © 2015 John Wiley & Sons, Ltd.

Copyright 2016 Elsevier B.V., All rights reserved.


  • induced L norm
  • linear parameter-varying systems
  • periodic linear time-varying systems


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