DESIGN OF UNKNOWN INPUT FRACTIONAL-ORDER OBSERVERS FOR FRACTIONAL-ORDER SYSTEMS
This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order a satisfying 0 < alpha < 2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach, where the fractional order a belongs to 1 <= alpha < 2 and 0 < alpha <= 1, respectively. A stability analysis of the fractional-order error system is made and it is shown that the fractional-order observers are as stable as their integer order counterpart and guarantee better convergence of the estimation error.
unknown input fractional-order observers fractional-order systems stability linear matrix inequality fractional calculus existence condition