Robustness analysis of linear parameter varying systems using integral quadratic constraints

Research output: Contribution to journalResearch articleContributedpeer-review


  • Harald Pfifer - , University of Minnesota System (Author)
  • Peter Seiler - (Author)


A general approach is presented to analyze the worst case input/output gain for an interconnection of a linear parameter varying (LPV) system and an uncertain or nonlinear element. The LPV system is described by state matrices that have an arbitrary, that is not necessarily rational, dependence on the parameters. The input/output behavior of the nonlinear/uncertain block is described by an integral quadratic constraint (IQC). A dissipation inequality is proposed to compute an upper bound for this gain. This worst-case gain condition can be formulated as a semidefinite program and efficiently solved using available optimization software. Moreover, it is shown that this new condition is a generalization of the well-known bounded real lemma type result for LPV systems. The results contained in this paper complement known results that apply IQCs for analysis of LPV systems whose state matrices have a rational dependence on the parameters. The effectiveness of the proposed method is demonstrated on simple numerical examples.


Original languageEnglish
Pages (from-to)2843-2864
Number of pages22
JournalInternational journal of robust and nonlinear control
Issue number15
Publication statusPublished - 1 Oct 2015
Externally publishedYes

External IDs

Scopus 85028204547
ORCID /0000-0001-6734-704X/work/142235731



  • linear parameter varying systems, robust control, uncertain systems