Observer with Improved Convergence for a Class of Initialized FO-LTI Systems

In this contribution we investigate on the observer design for linear fractional-order (FO) systems which are excited by an unknown input in the past. The systems are assumed to have an order of differentiation less than one. We use an associated system of double-order of integration and design an unknown-input observer UIO) for this system such that a part of the memory effect is compensated. The higher order of differentiation also leads to an improved convergence of the estimation error. We present necessary and sufficient conditions for the existence of such unknown input observer. As a special case we investigate the order ‘one half’. In this case the estimation error decays exponentially and the entire memory is rejected in the integer-order error dynamics.