Both States and Unknown Inputs Simultaneous Estimation for Fractional-Order Linear Systems.

This article is devoted to estimating simultaneously both the states and the inputs of linear time-invariant fractional-order systems (LTI-FOSs) with the order 0 < α < 2 . Firstly, a necessary and sufficient stability criterion for LTI-FOSs with the order 0 < α < 1 is derived by the linear matrix inequality technique. Secondly, a novel fractional-order observer combined with state vectors and ancillary vectors is given, which can generalize several forms of existing observers. Moreover, the parameter matrices of the desired observer for both the order 0 < α < 1 and 1 < α < 2 are solved on the basis of the stability theorem and the solution to the generalized inverse matrix. Finally, the fractional-order observer design algorithm is proposed and then applied to an illustrated example, in which the simulation results are reported to verify the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]