Adaptive optics (AO) is a proven technique to correct turbulence on ground-based astronomical telescopes. The corrected Field of View (FoV) is however limited by the anisoplanatism effect. To extend the FoV, new Wide Field AO (WFAO) concepts have been recently developed. They aim at providing a wide FoV correction through the use of multi-guide-star WaveFront Sensors (WFSs) and several Deformable Mirrors (DMs). Such WFAO systems require a tomographic reconstruction of the atmospheric turbulence, leading to a multivariable problem of much higher complexity than in classic AO. They also raise new questions in terms of calibration and control. The Linear Quadratic Gaussian (LQG) control formalism is a natural way to cope with this issue. It enables both tomographic reconstruction and distinction between controlled output and measurements. In this paper, LQG control is presented and applied to WFAO systems. Performance is evaluated thanks to simulations based on theoretical studies, but also through laboratory experiments. We present the first results of the implementation of LQG control on a WFAO system, the HOMER bench, that has been developed recently at ONERA and which is devoted to WFAO laboratory research.