On the Control of Unstable First Order Linear Systems with Large Time Lag: Observer Based Approach

This work considers the problem of stabilization and control of a class of unstable first order linear systems subject to a relatively large input–output delay. As a first step, the conditions to ensure the stability of the system in closed loop with an output injection strategy are presented. In a second step, the stability conditions are used to design an observer-based scheme that provides a forward output estimation together with a feedback compensation to guarantee prediction convergence. The robustness of the overall observer-based strategy is analyzed when considering uncertainties on the magnitude of the time delay associated with the plant and the one considered on the design of the observer. A stability region as a function of these two time delays is obtained. The proposed prediction scheme is complemented by the use of a PI compensator to track step reference signals and to reject step disturbances.