The popularity of high and ultra-high definition displays has led to the need for methods to improve the quality of videos already obtained at much lower resolutions. Current Video Super-Resolution methods are not robust to mismatch between training and testing degradation models since they are trained against a single degradation model (usually bicubic downsampling). This causes their performance to deteriorate in real-life applications. At the same time, the use of only the Mean Squared Error during learning causes the resulting images to be too smooth. In this work we propose a new Convolutional Neural Network for video super resolution which is robust to multiple degradation models. During training, which is performed on a large dataset of scenes with slow and fast motions, it uses the pseudo-inverse image formation model as part of the network architecture in conjunction with perceptual losses, in addition to a smoothness constraint that eliminates the artifacts originating from these perceptual losses. The experimental validation shows that our approach outperforms current state-of-the-art methods and is robust to multiple degradations.