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arXiv · 2303.08465

On solving infinite-dimensional Toeplitz Block LMIs

Flora Vernerey·Pierre Riedinger·Jamal Daafouz
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Abstract

This paper focuses on the resolution of infinite-dimensional Toeplitz Block LMIs, which are frequently encountered in the context of stability analysis and control design problems formulated in the harmonic framework. We propose a consistent truncation method that makes this infinite dimensional problem tractable and demonstrate that a solution to the truncated problem can always be found at any order, provided that the original infinite-dimensional Toeplitz Block LMI problem is feasible. Using this approach, we illustrate how the infinite dimensional solution to a Toeplitz Block LMI based convex optimization problem can be recovered up to an arbitrarily small error, by solving a finite dimensional truncated problem. The obtained results are applied to stability analysis and harmonic LQR for linear time periodic (LTP) systems.

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Flora Vernerey, Pierre Riedinger, Jamal Daafouz. 2023-03-15. On solving infinite-dimensional Toeplitz Block LMIs. https://arxiv.org/abs/2303.08465

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