Asymptotic estimation of state and faults for linear systems with unknown perturbations

It is challenging to achieve asymptotic estimation of state and actuator faults for systems with unknown perturbations in both the state dynamics and output measurements. To address this, an adaptive sliding mode unknown input observer (ASMUIO) is developed under a mild rank condition of the perturbation distribution matrices. The key idea is to estimate the perturbations simultaneously with the state and faults, which then vanishes the perturbation effects from the estimation error dynamics. Existence conditions and rigorous feasibility proof of the proposed ASMUIO are given. A simulation example is provided to demonstrate the design efficacy in comparison with existing approaches