__Switched linear differential systems__

The well-known state-space paradigm for the analysis of systems with switching dynamics has been predominant in control theory. However, in many cases this framework is not justified from the physical point of view, since first principles models do not necessarily satisfy a global first-order differential structure. An example of this situation can be easily found when the changing laws of a switched system do not share the same state space, e.g. a power converter with multiple (dis-)connectable loads. Moreover, in the analysis of complex electrical networks, first principle models are more satisfactorily represented by impedances which naturally lead to sets of higher-order differential equations. Prompted by these issues, we have developed a new approach to switched systems based on behavioral system theory which is a trajectory-oriented rather than a represention-based approach. This framework permits to accomodate first principle equations, possibly of higher-order, without resorting to the use of pre-defined mathematical structures and thus circumventing the need to add fictitious variables and equations to analyze the system. Modeling, stability analysis, control and applications in power electronics are currently the main objectives in our scientific agenda.

__HVDC transmission systems__

Power electronics has enabled the possibility to handle high voltage direct current (HVDC) transmission, providing a set of convenient features such as enhanced stability, bidirection power flow control, high efficiency at long distances, flexible system synchronization among many other comepelling advantages for power systems. We are currently working on the development of modular multilevel converters and their associated control systems, as well as in the stability analysis of multi-terminal HVDC systems.

__Design of new DC-DC power converter topologies__

The design of new power converter topologies is of major importance in power electronics, since traditional topologies have limited gains, efficiency, etc., with respect to the requirements of emerging technologies such as renewable energy systems. In this research direction we focus on the development of converters with high voltage gains, highefficiency, current and voltage ripple mitigation, low-cost and small package implementation, etc. Examples of the technologies on which we are continuously working are switched capacitor, resonant, interleaved and multilevel DC-DC converters.