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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.
The paper deals with the problem of designing filters for non-linear discrete-time stochastic systems. In particular, it is shown how to design an unknown input filter for a single (constant) unknown input distribution matrix, which guarantees that the effect of a fault will not be decoupled from the residual. Subsequently, the problem of using one, fixed disturbance distribution matrix is eliminatek by using the interacting multiple models algorithm to select an appropriate unknown input distribution matrix from a predefined set of matrices. The final part of the paper shows an illustrative example, which confirms the effectiveness of the proposed approach.
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