A Comparative Study on H Resilient Observer Design; Lipschitz and One-sided Lipschitz Fractional Order Systems’ State Estimation

This paper proposes the states estimation of one-sided Lipschitz fractional order systems. In this regard, using an LMI based continuous frequency distribution results in H nonlinear resilient observer design in the presence of an exogenous disturbance input and observer's gain perturbation. Since one-sided Lipschitz class of nonlinear systems encompasses a wide range of nonlinearities including the Lipschitz class, It is shown that the proposed observer design based on the one-sided Lipschitz systems has simpler LMI and it can tolerate a wide range of changes in gains perturbation and exogenous disturbances compared to recent research findings for the counterpart Lipschitz systems. Finally, a financial fractional order system with Lipschitz nonlinearity is presented as an example, which can illustrate the effectiveness of the proposed one-sided Lipschitz observer design and compare the feasible region of input disturbance and observer’s gain for both Lipschitz and one-sided Lipschitz observer design.