This book focuses on the design and analysis of the control of voltage source converters connected to the grid through LCL filters from a Robust Control Theory approach. Particularly it is centred on grids presenting uncertainty in their intrinsic dynamic parameters and their influence over the inner control loop of a grid converter: the current control. To that end, the thesis follows a three-fold discussion. First part of this book studies the assumed grid model, its uncertain parameters and presents a proposal to recursively estimate them. The influence of those uncertain parameters over the stability of the current control loop of grid converters is the second topic of this document. Finally, after that analysis, the book deals with the complementary problem: the design of a robust controller for grid converters connected through LCL filters to grids whose parameters range between known values.