  State-of-the-art techniques for modeling, analysis and control of three-phase
electrical systems belong to the real-valued multi-input/multi-output (MIMO)
domain, or to the complex-valued nonlinear single-input/single-output (SISO)
domain. In order to complement both domains while simplifying complexity and
offering new analysis and design perspectives, this paper introduces the
application of geometric algebra (GA) principles to the modeling, analysis and
control of three-phase electrical systems. The key contribution for the
modeling part is the identification of the transformation that allows
transferring real-valued linear MIMO systems into GA-valued linear SISO
representations (with independence of having a balanced or unbalanced system).
Closed-loop stability analysis in the new space is addressed by using intrinsic
properties of GA. In addition, a recipe for designing stabilizing and
decoupling GA-valued controllers is provided. Numerical examples illustrate key
developments and experiments corroborate the main findings.
