Robust adaptive observer for fractional order nonlinear systems: An LMI approach

This paper is concerned with the parameter and state estimation problem in the presence of the observer gain perturbations for a class of fractional order nonlinear systems which are linear in the unknown parameters and nonlinear in the states. According to the equivalent frequency distributed model of fractional integrator, the direct Lyapunov approach is adopted to derive a nonlinear adaptive non-fragile observer. The gain for the non-fragile observer is systematically obtained in terms of linear matrix inequality (LMI). A numerical example is provided to illustrate the efficiency and validity of the proposed approach.