J. Almada, R. Leão, R. Sampaio, and G. Barroso, A centralized and heuristic approach for energy management of an AC microgrid, Renewable and Sustainable Energy Reviews, vol.60, pp.1396-1404, 2016.

U. Manandhar, A. Ukil, and T. Jonathan, Efficiency comparison of dc and ac microgrid, IEEE Innovative Smart Grid Technologies-Asia, pp.1-6, 2015.

R. O. Caceres and I. Barbi, A boost dc-ac converter: analysis, design, and experimentation, IEEE Trans. on Power Electronics, vol.14, issue.1, 1999.

G. Escobar, R. Ortega, H. Sira-ramirez, J. P. Vilain, and I. Zein, An experimental comparison of several nonlinear controllers for power converters, In proceedings of the IEEE Conference on Decision and Control, vol.1, pp.227-228, 1997.

P. S. Gurpide, O. A. Sadaba, L. M. Palomo, T. Meynard, and E. Lefeuvre, IEEE Annual Power Electronics Specialists Conference, vol.2, pp.974-979, 2001.

P. Sanchis, A. Ursaea, E. Gubia, and L. Marroyo, Boost DC-AC inverter: a new 340 control strategy, vol.20, pp.343-353, 2005.

M. Bajaj, V. Dwivedi, A. Bansal, P. Sarkar, and R. Kumar, Design and controlling of proposed efficient boost-inverter implemented using boost dc-dc converter, International Journal of Advanced Research in Electronics and Communication Engineering, vol.2

N. Vazquez, J. Alvarez, C. Aguilar, and J. Arau, Some critical aspects in sliding mode control design for the boost inverter, In proceedings of the IEEE Power Electronics Congress, pp.76-81, 1998.

D. Cortes, N. Vazquez, and J. Alvarez-gallegos, Dynamical sliding-mode control of the boost inverter, IEEE Trans. on Industrial Electronics, vol.56, issue.9, pp.3467-3476, 2009.

C. Albea, F. Gordillo, C. Canudas-de, and W. , Adaptive control design for a boost inverter, Control Engineering Practice, vol.19, issue.1, pp.32-44, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00531760

H. Flores-bahamonde, F. Valderrama-blavi, and J. M. Bosque-moncusi, , vol.355

G. García and L. Martínez-salamero, Using the sliding-mode control approach for analysis and design of the boost inverter, IET Power Electronics, vol.9, issue.8, pp.1625-1634, 2016.

R. Goebel, R. G. Sanfelice, and A. R. Teel, Hybrid Dynamical Systems: modeling, stability, and robustness, p.360, 2012.

G. Deaecto, J. Geromel, F. Garcia, and J. Pomilio, Switched affine systems control design with application to DC-DC converters, IET control theory & applications, vol.4, issue.7, pp.1201-1210, 2010.

C. Sanchez, G. Garcia, and L. Zaccarian, Hybrid dynamic modeling and control of switched affine systems: application to DC-DC converters, IEEE Conference on Decision and Control (CDC), vol.365, pp.2264-2269, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01220447

C. Sanchez, G. Garcia, S. Hadjeras, W. Heemels, and L. Zaccarian, Practical stabilisation of switched affine systems with dwell-time guarantees, IEEE Trans. on Automatic Control, vol.64, issue.11, pp.4811-4817, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01617999

C. Sanchez, O. Santos, D. Zambrano, F. Gordillo, and G. Garcia, On the practical stability of hybrid control algorithm with minimum dwell time for a DC-AC converter, IEEE Trans. on Control System Technology, vol.27, issue.6, pp.2581-2588, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01730522

E. Feron, Quadratic stabilizability of switched systems via state and output 375 feedback, 1996.

S. Solyom and A. Rantzer, The servo problem for piecewise linear systems

A. Coddington and R. Carlson, Linear Ordinary Differential Equations, vol.57, 1997.

I. Jikuya and I. Hodaka, Time domain analysis of steady state response in linear periodic systems and its application to switching converters, IFAC Proceedings Volumes, vol.44, pp.1307-1312, 2011.

R. G. Sanfelice, D. Copp, and P. A. Nanez, A toolbox for simulation of hybrid systems in Matlab/Simulink: Hybrid equations (HyEQ) toolbox, Hybrid Systems: Computation and Control Conference, vol.385, 2013.