Robust and Adaptive Fractional-Order Observer Design for One-sided Lipschitz Systems

This paper presents adaptive observer design for one-sided Lipschitz systems. One-sided Lipschitz systems are a wide branch of nonlinear systems that include Lipschitz systems. Designed observer simultaneously estimate states and unknown parameters of the system and it is robust against input perturbation and limited observer gain disturbance. As using  observer will results in having desirable performance besides observer stability, a non-fragile  observer is presented and its stability is investigated based on Lyapunov theorem. Using linear matrix inequality causes minimizing the effect of disturbance on the estimation error addition to calculating the observer’s gain systematically. Two examples are presented to show the efficiently and performance of the proposed observer and comparison with a new research in this field. Finally the conclusion of the paper and the useful suggestions for future researches in this field is presented.