  In this chapter some results related to Shunt Active Filters (SAFs) and
obtained by the authors and some coauthors are reported. SAFs are complex power
electronics equipments adopted to compensate for cur-rent harmonic pollution in
electric mains, due to nonlinear loads. By using a proper "floating" capacitor
as energy reservoir, the SAF purpose is to inject in the line grid currents
canceling the polluting har-monics. Control algorithms play a key role for such
devices and, in general, in many power electronics applications. Moreover,
systems theory is crucial, since it is the mathematical tool that enables a
deep understanding of the involved dynamics of such systems, allowing a correct
dimensioning, beside an effective control. As a matter of facts, current
injection objective can be straightforwardly formulated as an output tracking
control problem. In this fashion, the structural and insidious
marginally-stable internal/zero dynamics of SAFs can be immediately highlighted
and characterized in terms of sizing and control issues. For what concerns the
control design strictly, time-scale separation among output and internal
dynamics can be effectively exploited to split the control design in different
stages that can be later aggregated, by using singular perturbation analysis.
In addition, for robust asymptotic output tracking the Internal Model Principle
is adopted.
