On the determination of numerical control for two time scale continuous system

The multi-time-scale systems are subject of a great number of research works concerning their reduction and simplification, in order to elaborate the control. The singular perturbations theory is perfectly adapted to systems presenting multi-time-scale. The multi-time-scale property is due to the presence of slow and fast dynamic phenomena. The use of singular perturbations permits the decomposition of the global system in two sub-systems giving prominence to slow and fast parts. So, the determination of the control from these systems is faster than its calculation from the global one