Robust observer‐based‐controller design for uncertain fractional‐order time‐varying‐delay systems

Abstract

AbstractThis article focuses on the robust observer‐based controller (‐ROBC) for Uncertain Fractional‐Order Systems with Time‐Varying‐Delay (DU‐FOS‐TVD). First, the existence conditions of ‐ROBC are given. Then, based on the diffusive representation of the fractional‐order derivative and the indirect Lyapunov approach, a new sufficient condition is obtained and presented as a convex optimization problem with a Linear Matrix Inequality (LMI) constraint, which guarantees the robust stability of the estimation errors and the stabilization of the DU‐FOS‐TVD simultaneously. All observer matrices gains and control laws can be computed by solving the given LMI. A Numerical example is given to illustrate the validity of the proposed method.