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 language | English |
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Pages (from-to) | 5584 - 5590 |
Number of pages | 7 |
Journal | IEEE Transactions on Automatic Control |
Volume | 69 |
Issue number | 8 |
Early online date | 28 Feb 2024 |
DOIs | |
Publication status | Published - 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