The Non-Strict Projection Lemma

T.J. Meijer (Corresponding author), T. Holicki, S.J.A.M. van den Eijnden, C.W. Scherer, W.P.M.H. Heemels

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)

Abstract

The projection lemma (often also referred to as the elimination lemma) is one of the most powerful and useful tools in the context of linear matrix inequalities for system analysis and control. In its traditional formulation, the projection lemma only applies to strict inequalities, however, in many applications, we naturally encounter non-strict inequalities. As such, we present, in this article, a non-strict projection lemma that generalizes both its original strict formulation as well as an earlier non-strict version. We demonstrate several applications of our result in robust linear matrix inequality-based marginal stability analysis and stabilization, a matrix S-lemma, which is useful in (direct) data-driven control applications, and matrix dilation.

Original languageEnglish
Pages (from-to)5584 - 5590
Number of pages7
JournalIEEE Transactions on Automatic Control
Volume69
Issue number8
Early online date28 Feb 2024
DOIs
Publication statusPublished - Aug 2024

Funding

This work was supported by the European Research Council (ERC) through the Advanced ERC grant agreement PROACTHIS under Grant 101055384. The work of Tobias Holicki and Carsten W. Scherer was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy EXC 2075 - 390740016. They acknowledge the support by the Stuttgart Center for Simulation Science (SimTech).

Keywords

  • Asymptotic stability
  • Control design
  • Data-driven control
  • Interpolation
  • Linear matrix inequalities
  • linear matrix inequalities (LMIs)
  • Linear systems
  • marginal stability
  • parameter elimination
  • Robust control
  • semi-definite programming
  • Symmetric matrices
  • semidefinite programming

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