With the increasingly rapid penetration of power electronics into AC grid, there is an urgent need in enhancing stability and performance of grid-connected converters. An advanced $H_{\infty}$ multi-input multi-output (MIMO) control using linear matrix inequality (LMI) techniques is introduced and applied for electromagnetic transient (EMT) three-phase voltage source converter (VSC) grid-connected system (simple STATCOM). The proposed control is compared with classical cascade vector control through a validation test of short-circuit event. The comparison results prove that the advanced control approach provides much better performance and transient behaviour compared to classic vector controls, as a result of using $H_{\infty}$ optimization technique to minimize the effect of frequency's and grid voltage's variations. The validation test is done using MATLAB Simscape in EMT simulation, and also gives a step-by-step path of implementation for applying advanced control in industrial-level application of power converter. These results will be further used to control the units of the new concept of \textit{Dynamic Virtual Power Plant} introduced in the H2020 POSYTYF project.