Fault detection observer design for fractional-order systems

The aim of this paper is to investigate the fault detection observer design problem for fractional-order systems. Firstly, the performance index H
_-
/H
_∞
of integer-order systems is generalized to fractional-order systems, and the fault detection problem is formulated as designing a fault detection observer subject to three conditions: system stability condition, fault sensitivity condition and disturbance robustness condition. Secondly, two theorems about the performance index H
_-
/H
_∞
are given and then the sufficient condition for designing the fault detection observer subject to the above three conditions is derived in terms of linear matrix inequalities. Finally, an illustrative example demonstrates the validity of the proposed theoretical results.