Closed-loop stability analysis of time-delayed first-order systems under generalized predictive control

The necessary and sufficient conditions are established for the closed-loop stability of generalized predictive control (GPC) applied to first order systems with time-delay by combining parametric and non-parametric models. It is shown that: (1) if the open-loop system is stable, then there must be a controller such that the closed-loop system will remain stable whatever the open-loop gain K and the time constant T change into; (2) while if the open-loop system is unstable, then whatever the controller parameters are chosen, the closed-loop stability will be lost when K and T go out of the stability region.