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, Tome 23 (2013) no. 3, pp. 491-500.

Résumé

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.

Détail

Keywords: fractional calculus, fractional order systems, fractional order observers, existence condition, linear matrix inequality, unknown input, stability
Mots-clés : ułamkowy rachunek różniczkowy, układ ułamkowego rzędu, liniowa nierówność macierzowa

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