A matrix-exponential predictive ESO-based control for linear systems with output delay and uncertainty

This paper presents a matrix-exponential predictive extended state observer (MEP-ESO) based Linear Active Disturbance Rejection Control (LADRC) scheme for linear systems with output delay and uncertainty. The proposed method employs a two-stage cascade observer structure: a zeroth-order observer estimates the delayed extended state, and a first-order observer propagates the zeroth-order observer's estimate via the matrix exponential to predict the current state. This design eliminates the numerical integration required in conventional extended state predictor observer (ESPO). In addition, it uses a single gain vector shared by both cascade stages, reducing tuning to a single bandwidth parameter. Comparative simulation results verify that the proposed approach yields better tracking accuracy, shorter settling time, and stronger disturbance rejection than conventional delayed designed ADRC (DD-LADRC) and Smith predictor based ADRC (SP-LADRC). The presented method provides a simple, effective, and practical solution for robust control of delayed linear systems in industrial applications.