The Non-Strict Projection Lemma introduces a powerful tool for system analysis and control, extending beyond traditional strict inequalities. The article presents a new non-strict projection lemma that encompasses both the original strict formulation and an earlier non-strict version. This generalization allows for various applications in robust linear-matrix-inequality-based marginal stability analysis, stabilization, matrix S-lemma, and matrix dilation. The authors illustrate how this novel lemma can be applied to solve complex control problems by providing necessary and sufficient conditions for the existence of solutions to certain LMIs. By demonstrating several practical applications of the non-strict projection lemma, including LMI-based marginal stability conditions and matrix dilation problems, the authors showcase its versatility and significance in modern control theory.
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by T.J. Meijer,... om arxiv.org 03-18-2024
https://arxiv.org/pdf/2305.08735.pdfDiepere vragen