Geodesic
On some relaxations commonly used in the study of linear systems
Kybernetika, Tome 51 (2015) no. 5, pp. 830-855.

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This note proposes a quite general mathematical proposition which can be a starting point to prove many well-known results encountered while studying the theory of linear systems through matrix inequalities, including the S-procedure, the projection lemma and few others. Moreover, the problem of robustness with respect to several parameter uncertainties is revisited owing to this new theorem, leading to LMI (Linear Matrix Inequality)-based conditions for robust stability or performance analysis with respect to ILFR (Implicit Linear Fractional Representation)-based parametric uncertainty. These conditions, though conservative, are computationally very tractable and make a good compromise between conservatism and engineering applicability.
DOI : 10.14736/kyb-2015-5-0830
Classification : 93C05, 93C35, 93D09
Keywords: LMI relaxations; robust analysis; parametric uncertainty 
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Bachelier, Olivier; Mehdi, Driss. On some relaxations commonly used in the study of linear systems. Kybernetika, Tome 51 (2015) no. 5, pp. 830-855. doi : 10.14736/kyb-2015-5-0830. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2015-5-0830/

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