Abstract
Passification-based adaptive control, also known as simple adaptive control, is studied with respect to its robustness to time-varying uncertainties. Results are formulated in terms of LMIs and are therefore testable in polynomial time using semi-definite programming solvers. The main result shows that the adaptive strategy allows, without measurement nor estimation of the uncertain parameters to guarantee asymptotic stability for a wide rage of these parameters. To achieve this result, the stability property is relaxed: convergence is proved to a small neighborhood of the origin, and attractive domain. It is also demonstrated that this attractor can be made as small as required the only limitation being implementation constraints.
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Original Russian Text © D. Peaucelle, H.M. Khan, P.V. Pakshin, 2009, published in Avtomatika i Telemekhanika, 2009, No. 9, pp. 113–127.
This work was supported by the Russian Foundation for Basic Research, project no.07-01-92166-NTSNI_a, and by CNRS-RFBR research cooperation, project no.PI CS 4281.
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Peaucelle, D., Khan, H.M. & Pakshin, P.V. LMI-based analysis of robust adaptive control for linear systems with time-varying uncertainty. Autom Remote Control 70, 1540–1552 (2009). https://doi.org/10.1134/S0005117909090070
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DOI: https://doi.org/10.1134/S0005117909090070