  A classical approach to design controllers for interconnected systems is to
assume that the different subsystems operate at different time scales, then
design simpler controllers within each time scale, and finally certify
stability of the interconnected system via singular perturbation analysis. In
this work, we propose an alternative approach that also allows to design the
controllers of the individual subsystems separately. However, instead of
requiring a sufficiently large time-scale separation, our approach consists of
adding a feed-forward term to modify the dynamics of faster systems in order to
anticipate the dynamics of slower ones. We present several examples in bilevel
optimization and cascade control design, where our approach improves the
performance of currently available methods.
