Non-fragile tracking controller design for fractional order systems against active disturbance rejection

In this work, a new non-fragile based tracking controller design for fractional order systems with non-linear uncertainty, unidentified external disturbances, and time-delay is investigated. A novel structure of a fractional order non-fragile repetitive controller is suggested to obtain the tracking performance for the addressed system. In particular, gain fluctuations are used with an improved two-degrees-of-freedom Smith predictor in the construction of this structure. Using the Lyapunov–Krasovskii stability theory and a continuous amplitude distributed equivalent system, a new set of criteria to determine the asymptotic stability of the associated closed-loop system is proposed in the context of linear matrix inequalities. Within a single framework, disturbance estimation, asymptotic tracking, and time delay compensation are all done using the obtained stability results. The resulting theoretical results are finally confirmed by numerical examples that demonstrate how the specified constraints could lead the system output to precisely match any defined reference signal by balancing for the unidentified exterior disturbance.