TY - GEN A1 - Schiffer, Johannes A1 - Efimov, Denis A1 - Ortega, Romeo T1 - Global synchronization analysis of droop-controlled microgrids—A multivariable cell structure approach T2 - Automatica N2 - The microgrid concept represents a promising approach to facilitate the large-scale integration of renewable energy sources. Motivated by this, the problem of global synchronization in droop-controlled microgrids with radial topology is considered. To this end, at first a necessary and sufficient condition for existence of equilibria is established in terms of the droop gains and the network parameters. Then, the local stability properties of the equilibria are characterized. Subsequently, sufficient conditions for almost global synchronization are derived by means of the multivariable cell structure approach recently proposed in Efimov and Schiffer (2019). The latter is an extension of the powerful cell structure principle developed by Leonov and Noldus to nonlinear systems that are periodic with respect to several state variables and possess multiple invariant solutions. The analysis is illustrated via numerical examples. KW - Global synchronization KW - controlled microgrids Y1 - 2019 UR - https://www.sciencedirect.com/science/article/pii/S000510981930411X U6 - https://doi.org/10.1016/j.automatica.2019.108550 SN - 0005-1098 IS - 109 ER - TY - GEN A1 - Efimov, Denis A1 - Schiffer, Johannes T1 - On boundedness of solutions of state periodic systems: a multivariable cell structure approach T2 - IEEE Transactions on Automatic Control N2 - Many dynamical systems are periodic with respect to several state variables. This periodicity typically leads to the coexistence of multiple invariant solutions (equilibria or limit cycles). As a consequence, while there are many classical techniques for analysis of boundedness and stability of such systems, most of these only permit to establish local properties. Motivated by this, a new sufficient criterion for global boundedness of solutions of such a class of nonlinear systems is presented. The proposed method is inspired by the cell structure approach developed by Leonov and Noldus and characterized by two main advances. First, the conventional cell structure framework is extended to the case of dynamics, which are periodic with respect to multiple states. Second, by introducing the notion of a Leonov function, the usual definiteness requirements of standard Lyapunov functions are relaxed to sign-indefinite functions. Furthermore, it is shown that under (mild) additional conditions the existence of a Leonov function also ensures input-to-state stability, i.e., robustness with respect to exogenous perturbations. The performance of the proposed approach is demonstrated via the global analysis of boundedness of trajectories for a nonlinear system. Y1 - 2019 U6 - https://doi.org/10.1109/TAC.2019.2892395 SN - 0018-9286 SN - 1558-2523 VL - 64 IS - 10 SP - 4094 EP - 4104 ER -