The notion of observability and detectability for a particular class of hybrid systems, linear continuous-time switching systems, is investigated. We compare some of the definitions of observability previously offered and we analyze their drawbacks. A novel definition of observability is prw posed corresponding to the possibility of reconstructing the state of the system from the howledge of the discrete and continuous outputs and inputs. The notion of detectability is also introduced. Sufficient and necessary conditions for these properties to hold for switching systems are presented.

Abstract-New connection constraints for the power network (Grid Codes) require more flexible and reliable systems, with robust solutions to cope with uncertainties and intermittence from renewable energy sources (renewables), such as photovoltaic arrays. The interconnection of such renewables with storage systems through a Direct Current (DC) MicroGrid can fulfill these requirements. A "Plug and Play" approach based on the "System of Systems" philosophy using distributed control methodologies is developed in the present work. This approach allows to interconnect a number of elements to a DC MicroGrid as power sources like photovoltaic arrays, storage systems in different time scales like batteries and supercapacitors, and loads like electric vehicles and the main AC grid. The proposed scheme can easily be scalable to a much larger number of elements.Note to Practitioners-Renewable energy can play a key role in producing local, clean and inexhaustible energy to supply the worlds increasing demand for electricity. Photovoltaic conversion of solar energy is a promising solution and is the best fit in several situations. However, its intermittent nature remains a real difficulty that can create instability. To answer to the new constraints of connection to the network (grid codes) for either solar plants than distributed generation, one possible solution is the use of Direct Current (DC) MicroGrids including storage systems, in order to integrate the electric power generated by these photovoltaic arrays. One of the main reasons is the fact that photovoltaic panels, batteries, supercapacitors and electric vehicles are DC. On the other hand, reliable stable control of DC MicroGrids is still an open problem. In particular it lacks rigorous analysis that can establish the operation regions and stability conditions for such MicroGrids. Current works that consider realistic grids usually apply from-the-shelf solutions that do not study the dynamics of such grids. While more rigorous studies just consider too much simplified grids that does not represent the conditions from real life applications. The present work presents nonlinear controllers capable to stabilize the DC MicroGrid, with rigorous analysis on the sufficient conditions and region of operation of the proposed control.

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