A performance index for input observer-based monitoring systems

The closed-loop state and input observer (CSIO) is a pole-placement type observer and estimates unknown state and input variables simultaneously. These pole-placement type observers may have poor performance with respect to ill-conditioning factors such as unknown initial estimates, round-off error, modeling error, sensing bias error etc. For the robust monitoring performance, the effects of these ill-conditioning factors must be minimized in designing the observers. In this paper, the transient and steady-state performance of the input observer is investigated quantitatively by considering the error bounds due to ill-conditioning factors. The closed-loop state and input observer with small performance indices are considered as a well-conditioned input observer. By considering both transient and steady-state performance indices, the main performance index is determined as the condition number of the observer eigenvector matrix based on L₂ norm.