Robustness and Safe Sampling of Distributed-Delay Control Laws for Unstable Delayed Systems

In the control of delayed systems by a finite spectrum assignment (FSA) , in the control law, the integral over the time delay of a function of past control appears. This assignment is in fact available for continuous delayed process independently of the stability of the latter, which is very interesting since Smith predictor is usually only used with stable processes. Nevertheless, in case of FSA control implementation, this integral control should be sampled so that spectrum assignment is not necessarily preserved and an unstable discrete closed loop can be obtained , . In this technical note, FSA integral control robustness with respect to prediction time uncertainty is analyzed for an unstable continuous linear system. A transformation approach is also proposed to understand the effects of different ways of sampling control laws. In a last part, a case study shows how Simpson approximation of integral control law leads to an unstable digital closed loop.