Kybernetika 51 no. 5, 830-855, 2015

On some relaxations commonly used in the study of linear systems

Olivier Bachelier and Driss MehdiDOI: 10.14736/kyb-2015-5-0830

Abstract:

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.

Keywords:

parametric uncertainty, LMI relaxations, robust analysis

Classification:

93C05, 93C35, 93D09

paper.pdf

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