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1 International Journal of Applied Mathematics and Computer Science

1 2013

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Design of unknown input fractional-order observers for fractional-order systems

N’Doye I., Darouach M., Voos H., Zasadzinski M.

International Journal of Applied Mathematics and Computer Science

2013

Vol. 23, no. 3

491--500

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 α satisfying 0 < α < 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 α belongs to 1 ≤ α < 2 and 0 < α ≤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.