Exponentially converging observer for a class of FO-LTI systems

In this contribution the observer design for a class of fractional-order linear systems (FO-LTI) is considered. We use an integer-order system associated with the original FO-LTI system and present necessary and sufficient conditions for its observability. Based on this analysis we propose a time-varying integer-order observer for the original fractional-order system. We propose an input-dependent state transformation which avoids singularities for discontinuous inputs. This allows for the real-time implementation of the observer. The estimation error of the proposed observer exhibits an exponential decay rate which is much faster than can be obtained by any linear FO-type Luenberger observer.