A new non-fragile H∞ proportional—integral filtered-error adaptive observer for a class of non-linear systems and its application to synchronous generators

Abstract

In this paper, a parameter and state estimation problem in the presence of observer gain perturbations and input disturbance is discussed for the Lipschitz systems that are linear in unknown parameters and non-linear in states. A non-linear non-fragile proportional—integral filtered-error adaptive observer is designed, and its stability conditions based on the Lyapunov technique are derived. The optimal gain among a solution set that satisfies the observer stability conditions is derived systematically using the linear matrix inequality approach. Numerical examples, as well as a synchronous generator case study, are provided in which the non-linear terms depend on the unmeasured states. The proposed design is more robust against both disturbance and gain perturbations than those presented in recent research. Moreover, it is feasible for much larger values of the Lipschitz constants than is the case for conventional methods.