## 5 Conclusions  
This paper develops a unified approach for the design of control laws for the power electronics converters. The control problems induced by the numerous practical cases of interest can be identified as a stabilization or as a tracking problem. To be able to derive a systematic approach for tackling them, the general bilinear power converter model is written in a specific way. Under some assumptions, satisfied for a large family of converters and necessary for the existence of a solution to the stated problems, stabilization or tracking control laws are proposed. They belong to the class of sliding mode controls, whose sliding surfaces, dependent on the problem under study, are systematically derived and ensure stability properties. All the methods are illustrated by numerous simulated examples for a large diversity of problems, some of them being non-trivial. The obtained results, highlighting their potential and their genericity level, are very promising. The next step in the near future is to apply these methods to a series of converter topologies involving a complete set of parasitic elements representing power losses and showing through experimental results that the deduced control laws can be implemented without any detriment caused by digital and analogue electronic devices limitations. Complementarily, these results could be compared with the ones obtained using other well established methods.  
From a theoretical point of view, several points need to be particularly investigated. Concerning the control of power converters, we see that there is a close connection between the original model and the relaxed one. This important connection ensures some kind of regularity and the main conclusion is that the original control laws, whose implementation could be difficult, can be approximated by control laws that could be seen as \"relaxed ones\", easier to implement and allowing to manage some important practical characteristics, such as switching frequency. This can be accomplished, for example, by space or time regularization techniques used in the context of the recently published hybrid control approach. Because of its practical implications, this point will particularly focus our attention.  
Another interesting work does not exclusively concern the control of power converters. It is possible to deduce from the bilinear model considered in this paper an equivalent  
Figure 8: Response to disturbances in the input voltage when a the converter feds a CPL.  
switched model, and then, in some sense, the controls proposed in this paper can be applied to the control of a certain class of switched affine linear systems. In that context, Lemma 1 shows that, for the class of systems whose modes or a convex combination of them are quadratically stable, such an assumption is systematically satisfied leading to the existence of a globally asymptotic stabilization switched control. An interesting work is to analyze deeply this assumption and try to characterize classes of switched systems satisfying it, even locally, with the objective of deducing stabilizing controls.  
To end, in the paper, it is supposed that the state is measurable, and thus it can be used in the control law. If only partial information is available, a method is to enforce the structure of the matrix \(P\) as done, for example, in [35]. However, in some cases, it is not possible to impose the needed structure to \(P\). If it happens, a method is to design an observer. This problem will be investigated following the main ideas proposed in this paper.  
All authors contributed equally to all the stages of the research process and the preparation of the manuscript. All authors have read and agreed to the published version of the manuscript. This research was developed with the partial support of the Ministerio de Ciencia, Tecnologia e Innovacion de Colombia (MinCiencias) under contract 018-2016 and the HisPaliS project supported by the Agence Nationale de la Recherce de France (ANR).  
The authors declare no conflict of interest.