Robust functional observer design for uncertain fractional-order time-varying delay systems

In this work, existence and design of Robust Functional Observer (RFO) for Uncertain Fractional-Order Systems with Time-Varying-Delay (UFOS-TVD) are addressed. Usually, when the considered system is under the effect of structured uncertainties, this kind of problems, referred as L-2-gain rejection, aims at designing a RFO minimizing a given cost function subject to L-2-gain rejection constraint, which means, the rejection of the uncertain states effect on the estimated errors. An LMI-based minimization problem for the robust stability is derived based on the indirect Lyapunov and Lyapunov-Krasovskii approaches. Finally, a simulation results are presented to illustrate the performance of the proposed methodology.