Fault estimation for a class of nonlinear systems using the improved intermediate estimator

This paper focused on fault estimation in Lipschitz nonlinear systems by providing an improved intermediate estimator (IIE). The core feature of an intermediate estimator is to simultaneously estimate the fault and states of the system without considering the matching condition. Since fault estimation is the first step of the process to compensate for its effect, the system performance can be further improved by making more accurate fault estimation. The structure of the nominal intermediate estimator (NIE) was modified by being inspired by the proportional-integral (PI) controller to improve the performance characteristics of the estimator, such as convergence rate, overshoot, and steady-state error. The estimation equation was assumed as such in the proposed estimator structure that the estimated fault would have a PI structure of the output estimation error. This has increased the number of design parameters, improving the estimator performance in transient and steady-state. The NIE can be indeed known as a particular case of the IIE since the proposed estimator benefits from all the advantages of an NIE while improving the estimation performance. The states of the error system were proven to be uniformly ultimately bounded according to Lyapunov stability theory and using the LMI method, as well as the appropriate selection of parameters. The analysis of the theory, simulation, and comparing the results of the proposed method with the NIE method reveal the capabilities and advantages of the proposed method.