@misc{MendozaAvilaEfimovMercadoUribeetal., author = {Mendoza-Avila, Jesus and Efimov, Denis and Mercado-Uribe, Angel and Schiffer, Johannes}, title = {On Relaxed Conditions of Integral ISS for Multistable Periodic Systems}, series = {Proceedings of the 2021 61st IEEE Conference on Decision and Control (CDC)}, journal = {Proceedings of the 2021 61st IEEE Conference on Decision and Control (CDC)}, pages = {6}, abstract = {A novel characterization of the integral Inputto- State Stability (iISS) property is introduced for multistable systems whose dynamics are periodic with respect to a part of the state. First, the concepts of iISS-Leonov functions and output smooth dissipativity are introduced, then their equivalence to the properties of bounded-energy-bounded-state and global attractiveness of solutions in the absence of disturbances are proven. The proposed approach permits to relax the usual requirements of positive definiteness and periodicity of the iISSLyapunov functions. Moreover, the usefulness of the theoretical results is illustrated by a robustness analysis of a nonlinear pendulum with a constant bias input and an unbounded statedependent input coefficient.}, language = {en} } @misc{MercadoUribeMendozaAvilaEfimovetal., author = {Mercado-Uribe, Angel and Mendoza-{\´A}vila, Jes{\´u}s and Efimov, Denis and Schiffer, Johannes}, title = {A Leonov Function for Almost Global Synchronization Conditions in Acyclic Networks of Heterogeneous Kuramoto Oscillators}, series = {IFAC-PapersOnLine}, volume = {56}, journal = {IFAC-PapersOnLine}, number = {2}, issn = {2405-8963}, doi = {10.1016/j.ifacol.2023.10.248}, pages = {9505 -- 9510}, abstract = {Sufficient conditions for almost global synchronization in acyclic networks of Kuramoto oscillators with heterogeneous coupling strengths and natural frequencies are presented. The result is established by employing the recently developed Leonov function framework for systems whose dynamics are periodic for all state variables. The synchronization property is accompanied by necessary and sufficient conditions to guarantee the existence of equilibria. The implications of these conditions on the network topology, the oscillator's coupling strengths and natural frequencies are discussed. Finally, the results are illustrated via a numerical example.}, language = {en} } @misc{MendozaAvilaMercadoUribeEfimovetal., author = {Mendoza-Avila, Jesus and Mercado-Uribe, Angel and Efimov, Denis and Schiffer, Johannes}, title = {Design of controls for ISS and Integral ISS Stabilization of Multistable State Periodic Systems}, series = {IFAC-PapersOnLine}, volume = {56}, journal = {IFAC-PapersOnLine}, number = {2}, doi = {https://doi.org/10.1016/j.ifacol.2023.10.936}, pages = {4472 -- 4477}, language = {en} } @misc{MendozaAvilaEfimovMercadoUribeetal., author = {Mendoza-Avila, Jesus and Efimov, Denis and Mercado-Uribe, Angel and Schiffer, Johannes}, title = {Design of Controls for Boundedness of Trajectories of Multistable State Periodic Systems}, series = {62nd IEEE Conference on Decision and Control (CDC), 2023}, journal = {62nd IEEE Conference on Decision and Control (CDC), 2023}, isbn = {979-8-3503-0124-3}, issn = {2576-2370}, doi = {10.1109/CDC49753.2023.10383528}, pages = {6}, language = {en} } @misc{MercadoUribeMendozaAvilaEfimovetal., author = {Mercado-Uribe, Angel and Mendoza-{\´A}vila, Jes{\´u}s and Efimov, Denis and Schiffer, Johannes}, title = {A Control Leonov Function Guaranteeing Global ISS of Two Coupled Synchronverters}, series = {62nd IEEE Conference on Decision and Control (CDC), 2023}, journal = {62nd IEEE Conference on Decision and Control (CDC), 2023}, isbn = {979-8-3503-0124-3}, issn = {2576-2370}, doi = {10.1109/CDC49753.2023.10383811}, pages = {6}, language = {en} } @misc{MercadoUribeMendozaAvilaEfimovetal., author = {Mercado-Uribe, Angel and Mendoza-{\´A}vila, Jes{\´u}s and Efimov, Denis and Schiffer, Johannes}, title = {Sufficient conditions for global boundedness of solutions for two coupled synchronverters}, series = {2024 IEEE 63rd Conference on Decision and Control (CDC)}, journal = {2024 IEEE 63rd Conference on Decision and Control (CDC)}, publisher = {IEEE}, address = {New York}, doi = {10.1109/CDC56724.2024.10886006}, pages = {2785 -- 2790}, abstract = {This paper analyzes two synchronverters connected in parallel to a common capacitive-resistive load through resistive-inductive power lines. This system is conceptualized as a microgrid with two renewable energy sources controlled using the synchronverter algorithm. It is modeled as an interconnection of three port-Hamiltonian systems, and the dq-coordinates model is derived by averaging the frequencies. Applying the recent Leonov function theory, sufficient conditions to guarantee the global boundedness of the whole system's trajectories are provided. This is necessary to reach the global synchronization of microgrids. Additionally, a numerical example illustrates the potential resonance behavior of the microgrid.}, language = {en} } @misc{MercadoUribeMendozaAvilaEfimovetal., author = {Mercado-Uribe, Angel and Mendoza-Avila, Jesus and Efimov, Denis and Schiffer, Johannes}, title = {Conditions for global synchronization in networks of heterogeneous Kuramoto oscillators}, series = {Automatica}, volume = {175}, journal = {Automatica}, publisher = {Elsevier BV}, address = {Amsterdam}, issn = {0005-1098}, doi = {10.1016/j.automatica.2025.112180}, pages = {1 -- 11}, abstract = {The Kuramoto model is essential for studying synchronization. In this work, we present sufficient conditions for global synchronization in networks of heterogeneous Kuramoto oscillators in the absence of homoclinic and heteroclinic cycles. The result is established by constructing a suitable Leonov function candidate for the Kuramoto model, which provides sufficient conditions for almost global synchronization in networks with acyclic and meshed topologies. The synchronization property is accompanied by necessary and sufficient conditions to guarantee the existence of equilibria, which are satisfied if the conditions for synchronization hold. The implications of the main conditions and their relationship with the network topology and parameters are discussed. Finally, the results are illustrated via a numerical example.}, language = {en} } @misc{Mendoza‐AvilaEfimovAngelMercado‐Uribeetal., author = {Mendoza-Avila, Jesus and Efimov, Denis and Angel Mercado-Uribe, Jose and Schiffer, Johannes}, title = {Design of control laws for robust global stabilization of multistable state periodic systems}, series = {International journal of robust and nonlinear control}, journal = {International journal of robust and nonlinear control}, publisher = {Wiley}, address = {New York, NY}, issn = {1049-8923}, doi = {10.1002/rnc.70206}, pages = {1 -- 20}, abstract = {This paper continues with the development of the input-to-state stability (ISS)-control Leonov function (CLeF) approach. The definitions of practical ISS and integral ISS (iISS)-CLeFs are refined, and the proposed methodology for control synthesis is improved to simplify the final control law. Then, it is shown that the existence of practical ISS- and iISS-CLeFs is a sufficient condition to guarantee the existence of a controller that endows multistable state periodic systems with the ISS and iISS properties, respectively. Furthermore, a methodology for the design of such a controller is provided via the well-known Sontag's universal formula. Besides, an extension of the main result is presented to connect the ISS-CLeF approach with the standard Leonov function method such that the maximal invariant set of the closed-loop system is compact on a manifold. Finally, the proposed approach is applied to the design of an excitation controller for a synchronous generator, which guarantees global ISS properties for the closed-loop system, unlike the usual local results reported in the literature. The obtained control is also independent of the load angle. The effectiveness of the designed controller is demonstrated in simulations.}, language = {en} }