Dynamic observer-based controllers for fractional-order linear systems with positive real uncertainty

This paper investigates the topic about robust dynamic observer-based controller design for fractional-order systems
$(0 < \alpha < 1)$
with positive real uncertainty. By constructing the linear variation of variables, even when the system and the input matrix are uncertain simultaneously, the conditions of designed the observer and controller gain can be obtained by solving a set of linear matrix inequalities (LMIs). Compared with Luenberger observer, the dynamic observer-based controller is another method without using equality constraints under LMI conditions.