H∞$$ {H}_{\infty } $$ filtering and reduced‐order optimization methods for control of time‐delay linear systems with unknown disturbances and faults

Abstract

SummaryIn this paper, the problem of state and fault estimations for a class of linear time‐delay systems is studied, whose state and output are affected by delays and unknown disturbances. To solve this problem, two methods of observer design are proposed in this paper. One is a new sliding mode observer (SMO) based on proper system transformation and filter, the asymptotic stability of state and fault estimation error can be guaranteed. The second one is an adaptive sliding‐mode unknown input observer (ASMUIO), which is developed under the medium rank of the perturbation distribution matrix to estimate the disturbance simultaneously with the state and fault, and then to eliminate the disturbance effect from the estimation error systems. The conditions for the existence of the proposed SMO and ASMUIO and the strict proof of their feasibility are presented. Two numerical examples are given to illustrate the effectiveness of the new methods.