Robust controllers in disturbance decoupling of uncertain max-plus linear systems: an application to a high throughput screening system for drug discovery

This paper presents robust controllers solving the disturbance decoupling problem(DDP) of a class of uncertain max-plus linear systems, whose system matrices vary between intervals with known lower and upper bounds. The DDP for such uncertain max-plus linear systems is defined as finding a control interval such that the output trajectory interval for the disturbed controlled system belongs to the output trajectory interval for the undisturbed controlled system. In other words, the controls are able to absorb the effects of disturbances robustly for such systems. Both of the open-loop control intervals and the output feedback control intervals solving the DDP are constructed using the residuation theory and proved to be optimal for the just-in-time control criterion. The main results of this paper are illustrated by a high throughput screening system for drug discovery.