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

Abstract

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
Volume26
Issue number4
DOIs
StatePublished - Mar 10 2016

Keywords

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

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