Communication Dans Un Congrès Année : 2023

On solving infinite-dimensional Toeplitz Block LMIs

Résumé

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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Dates et versions

hal-04026852 , version 1 (14-03-2023)
hal-04026852 , version 2 (29-04-2023)
hal-04026852 , version 3 (05-05-2023)

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Flora Vernerey, Pierre Riedinger, Jamal Daafouz. On solving infinite-dimensional Toeplitz Block LMIs. The 62nd IEEE Conference on Decision and Control (CDC 2023), IEEE, Dec 2023, Singapour, Singapore. ⟨hal-04026852v3⟩
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