Static Output Feedback Control with H∞ Performance for a Three-Phase Shunt Active Filter

This paper deals with the synthesis of a static output feedback control law with H
∞
performance for a three-phase shunt active power filter used to compensate current harmonics so that the network current remains quasi-sinusoidal and therefore electric power quality is improved. In a previous work, this system has been successfully driven by a state feedback controller. However, the main goal is to reduce the number of measured outputs. The objective of this work is the design of an output feedback H
∞
controller by non-iterative means. This can be easily achieved by imposing a block diagonal structure on the Lyapunov matrix in order to transform bilinear matrix inequalities into a convex optimization problem. The validity of the synthesized static gain is investigated through numerical simulations.