A new $H_{\infty}$ Observer for continuous LPV systems affected by Unknown Inputs

Abstract

The main contribution of this paper is the development of a H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> based state observer for noisy Linear Parameter Varying (LPV) systems affected by Unknown Inputs (UI). The observer is constructed in order to be unbiased (in particular the state estimation error is independent of the UI) and with a minimum L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> transfer between the perturbations (assumed to be with finite energy) and the estimation errors. Contrary to equivalent observers developed in the literature, the present one relaxes the classical rank condition widely used for the decoupling of the UI. In order to do so, High Order Sliding Modes (HOSM) differentiator are used. Finally, an example illustrates the theoretical contribution.