The goal of this paper is to develop a computationally tractable framework for data driven control of switched linear MIMO systems. Given a model structure and experimental data collected at different operating points, we seek to directly design a controller that stabilizes all plants compatible with this information, without an explicit plant identification. The main result of the paper shows that this problem can be recast into a polynomial optimization form and efficiently solved, leading to a robust controller with guaranteed l^∞ worse-case performance for any switching amongst all plants that could have generated the observed experimental data. The effectiveness of the proposed technique is illustrated with a numerical example.