The Non-Strict Projection Lemma

• 成果类型: Article
• 署名作者: Meijer, Tomas J.; Holicki, Tobias; van den Eijnden, Sebastiaan; Scherer, Carsten W.; Heemels, W. P. M. H. Maurice
• 署名单位: Eindhoven University of Technology; University of Stuttgart
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3371374
• 发表日期: 2024
• 页码: 5584-5590
• 关键词: Linear matrix inequalities; Symmetric matrices; asymptotic stability; Robust control; Linear systems; interpolation; control design; Data-driven control; Linear matrix inequalities (LMIs); marginal stability; parameter elimination; Semidefinite programming

摘要

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.