A new H∞ observer for continuous LPV systems with unknown inputs using an HOSM differentiator

Abstract

The main contribution of this paper is the development of $H_{\infty }$ state and unknown input (UI) observers for noisy linear parameter-varying (LPV) systems. The observers are constructed in order to be unbiased (in particular the state estimation error is decoupled from the UI) and with a minimum $L_{2}$ transfer between the perturbations (that are assumed to be with finite energy) and the estimation errors. Contrary to equivalent observers developed in the literature, the present one relaxes a widely used rank condition on the system matrices for decoupling the UI. In order to do so, high-order derivation is needed, which is done using a high-order sliding modes differentiator. A method is given to design observer gains for LPV systems under polytopic form. Finally, three examples illustrate some aspects of the theoretical contributions, and compare this work to the existing ones.