Fractional order PI observer for a class of fractional order systems

Abstract

Currently the study of fractional order systems has become of great research interest, in particular the state estimation stands out within the lines of studies for this type of systems. Different methodologies have been proposed in order to solve this problem, however most of the techniques involve complete information of the system. Thus, this work presents a methodology for state estimation in a class of fractional order systems based on a fractional order observer which is constructed through an algebraic technique. This observer presents some significant properties, for instance, only variables of interest are estimated, i.e., it is a non redundant observer, it does not need complete information of the system and the initial conditions for the observer can be freely assigned. The stability of this observer is analyzed with the global Mittag-Leffler boundedness approach. Finally, the effectiveness and accuracy of the proposed methodology is verified through state estimation of a fractional-order Duffing chaotic system.