On Interval Observer Design for Continuous-Time LPV Switched Systems

Chaima Zammali; Jérémy Van Gorp; Tarek Raissi

doi:10.14232/actacyb.24.3.2020.14

Chaima Zammali Conservatoire National des Arts et Métiers (CNAM), Cedric - Lab, HESAM Université, 292 Rue Saint-Martin, 75141 Paris Cedex 03, France https://orcid.org/0000-0002-8522-7276
Jérémy Van Gorp Conservatoire National des Arts et Métiers (CNAM), Cedric - Lab, HESAM Université, 292 Rue Saint-Martin, 75141 Paris Cedex 03, France https://orcid.org/0000-0002-0681-0026
Tarek Raissi Conservatoire National des Arts et Métiers (CNAM), Cedric - Lab, HESAM Université, 292 Rue Saint-Martin, 75141 Paris Cedex 03, France https://orcid.org/0000-0002-8735-9395

DOI: https://doi.org/10.14232/actacyb.24.3.2020.14

Keywords: interval observer, continuous-time LPV switched systems, polytopic parameter dependence, Lyapunov theory

Abstract

State estimation for switched systems with time-varying parameters has received a great attention during the past decades. In this paper, a new approach to design an interval observer for this class of systems is proposed. The scheduling vector is described by a convex combination so that the parametric uncertainties belong into polytopes. The considered system is also subject to measurement noise and state disturbances which are supposed to be unknown but bounded.
The proposed method guarantees both cooperativity and Input to State Stability (ISS) of the upper and lower observation errors. Sufficient conditions are given in terms of Linear Matrices Inequalities (LMIs) using a common quadratic Lyapunov function. Finally, a numerical example is provided to show the effectiveness of the designed observer.

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