Nonlinear Observer design for Systems with Sampled Measurements: An LPV Approach

Abstract

The aim of this work is to propose a design methodology of observers for a class of Lipschitz nonlinear dynamical systems with sampled measurements by using the differential mean value theorem (DMVT) which allows us to transform the nonlinear part of the estimation error dynamics into a linear parameter varying (LPV) system. The designed observer must ensure the stability of the estimation error subject to a sampled measurements. An LMI-based minimization problem is provided to ensure the stability and the existence of the observer using Lyapunov theory. Thus, the measurements sampling period is included in the LMI as a decision parameter. Indeed, this allows to widen the sampling period as much as possible, which helps optimization of energy consumption while guaranteeing the convergence of the observer. Finally, to illustrate the performance of the proposed methodology, a numerical example is presented.