<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We propose a new observer where the model, decomposed in generalized canonical form of regulation described by Fliess, is dissociated from the part assuring error correction. The obtained stable exact estimates give direct access to state variables in the form of successive derivatives. The dynamic response of the observer converges exponentially, as long as the nonlinearities are locally of Lipschitz type. In this case, we demonstrate that a quadratic Lyapunov function provides a number of inequalities which guarantee at least local stability. A synthesis of gains is proposed, independent of the observation time scale. Simulations of a Düffing system and a Lorenz strange attractor illustrate theoretical developments.</p></abstract>

We propose a new observer where the model, decomposed in generalized canonical form of regulation described by Fliess, is dissociated from the part assuring error correction. The obtained stable exact estimates give direct access to state variables in the form of successive derivatives. The dynamic response of the observer converges exponentially, as long as the nonlinearities are locally of Lipschitz type. In this case, we demonstrate that a quadratic Lyapunov function provides a number of inequalities which guarantee at least local stability. A synthesis of gains is proposed, independent of the observation time scale. Simulations of a Düffing system and a Lorenz strange attractor illustrate theoretical developments.

State estimation for MISO non–linear systems in controller canonical form

Laboratory of Inventive Design (LGECO), EA 3938 INSA Strasbourg, University of Strasbourg, 24 Boulevard de la Victoire, 67000 Strasbourg,

Laboratory of Engineering, Informatics and Imaging (ICUBE), University of Strasbourg, UMR 7357 CNRS, 2 Rue Boussingault, 67000 Strasbourg,

Nancy Research Center in Automatic (CRAN), UMR 7039, University of Lorraine, CNRS, 2 Avenue de Haye, 54516 Vandœuvre lès Nancy,

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"State estimation for MISO non\u2013linear systems in controller canonical form"}

We propose a new observer where the model, decomposed in generalized canonical form of regulation described by Fliess, is dissociated from the part assuring...

State estimation for MISO non–linear systems in controller canonical form

Published Online: Sep 29, 2016

Page range: 569 - 583

Received: Jun 19, 2015

Accepted: Jun 03, 2016

DOI: https://doi.org/10.1515/amcs-2016-0040

Keywords
non-linear systems, state observers, continuous time

© 2016 Benoît Schwaller et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

State estimation for MISO non–linear systems in controller canonical form

Published Online: Sep 29, 2016

Page range: 569 - 583

Received: Jun 19, 2015

Accepted: Jun 03, 2016

DOI: https://doi.org/10.1515/amcs-2016-0040

Keywordsnon-linear systems, state observers, continuous time

© 2016 Benoît Schwaller et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
non-linear systems, state observers, continuous time