Robust $H_{\infty }$ Observer-Based Control of Fractional-Order Systems With Gain Parametrization

This paper investigates the robust H_∞ observer-based control (OBC) for linear time-invariant disturbed uncertain fractional-order systems (DU-FOS). First, the existence conditions for robust H_∞ OBC are given. Then, based on the H_∞-norm analysis using the generalized Kalman-Yakubovich-Popov lemma for FOS, and following the fractional derivative order α, new sufficient linear matrix inequalities (LMIs) conditions are obtained to ensure the stability of the estimation errors and the stabilization of the DU-FOS simultaneously. All observer matrices gains and control laws can be computed by solving a unique LMI condition in one step. Numerical simulation is given to illustrate the validity of the proposed method.