10. Multi-scale systems and cascade controllers

Perturbation theory aims to eliminate short-term effects and retain only long-term effects. It links the trajectories of two systems with state spaces of different dimensions, the perturbed system having a greater number of states than the reduced system. This is an invaluable tool for building reduced models that summarize the essence of long-term qualitative behavior.

Generally speaking, there are two cases illustrated in figure 10 :

• first case: rapid effects stabilize very quickly, and are then referred to as singular disturbances, quasi-static approximation or adiabatic approximation (figure 10 a );...