Robust $\mathcal {H}_{\infty }$ State Feedback Controllers Based on Linear Matrix Inequalities Applied to Grid-Connected Converters

This paper provides robust H
_∞
state feedback controllers suitable for implementation in three-phase grid-connected converters. This control strategy is known to provide optimal rejection of disturbances, but usually leads to high control gains, that may be difficult to be implemented in practice. To mitigate this problem, a linear matrix inequality condition based on slack variables is proposed, which allows to impose bounds on the control gains in a less conservative way than conventional quadratic stability. The performance is proven to be superior to similar H
_∞
state feedback controllers in the literature, providing an upper bound for the converter output admittance and experimental grid currents complying with the IEEE Standard 1547.