TY - GEN A1 - Schiffer, Johannes A1 - Efimov, Denis T1 - Strong and Weak Leonov Functions for Global Boundedness of State Periodic Systems T2 - IEEE Transactions on Automatic Control N2 - We present new results for the analysis of global boundedness of state periodic systems. Thereby, we address both the case of systems, whose dynamics is periodic with respect to a part of the state vector, and the case of systems, whose dynamics is periodic with respect to all state variables. To derive the results, the notion of strong Leonov functions is introduced. The main results are complemented by a number of relaxations based on the concept of weak Leonov functions. Y1 - 2023 U6 - https://doi.org/10.1109/TAC.2023.3251903 SN - 0018-9286 SN - 1558-2523 VL - 68 IS - 12 SP - 7958 EP - 7965 ER - TY - GEN A1 - Mercado-Uribe, Angel A1 - Mendoza-Ávila, Jesús A1 - Efimov, Denis A1 - Schiffer, Johannes T1 - A Leonov Function for Almost Global Synchronization Conditions in Acyclic Networks of Heterogeneous Kuramoto Oscillators T2 - IFAC-PapersOnLine N2 - 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. Y1 - 2023 U6 - https://doi.org/10.1016/j.ifacol.2023.10.248 SN - 2405-8963 VL - 56 IS - 2 SP - 9505 EP - 9510 ER - TY - GEN A1 - Mendoza-Avila, Jesus A1 - Mercado-Uribe, Angel A1 - Efimov, Denis A1 - Schiffer, Johannes T1 - Design of controls for ISS and Integral ISS Stabilization of Multistable State Periodic Systems T2 - IFAC-PapersOnLine Y1 - 2023 U6 - https://doi.org/https://doi.org/10.1016/j.ifacol.2023.10.936 VL - 56 IS - 2 SP - 4472 EP - 4477 ER - TY - GEN A1 - Mendoza-Avila, Jesus A1 - Efimov, Denis A1 - Mercado-Uribe, Angel A1 - Schiffer, Johannes T1 - Design of Controls for Boundedness of Trajectories of Multistable State Periodic Systems T2 - 62nd IEEE Conference on Decision and Control (CDC), 2023 Y1 - 2023 SN - 979-8-3503-0124-3 SN - 979-8-3503-0123-6 U6 - https://doi.org/10.1109/CDC49753.2023.10383528 SN - 2576-2370 ER - TY - GEN A1 - Mercado-Uribe, Angel A1 - Mendoza-Ávila, Jesús A1 - Efimov, Denis A1 - Schiffer, Johannes T1 - A Control Leonov Function Guaranteeing Global ISS of Two Coupled Synchronverters T2 - 62nd IEEE Conference on Decision and Control (CDC), 2023 Y1 - 2023 SN - 979-8-3503-0124-3 SN - 979-8-3503-0123-6 U6 - https://doi.org/10.1109/CDC49753.2023.10383811 SN - 2576-2370 ER - TY - GEN A1 - Mercado-Uribe, Angel A1 - Mendoza-Ávila, Jesús A1 - Efimov, Denis A1 - Schiffer, Johannes T1 - Sufficient conditions for global boundedness of solutions for two coupled synchronverters T2 - 2024 IEEE 63rd Conference on Decision and Control (CDC) N2 - 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. Y1 - 2024 U6 - https://doi.org/10.1109/CDC56724.2024.10886006 SP - 2785 EP - 2790 PB - IEEE CY - New York ER - TY - GEN A1 - Mercado-Uribe, Angel A1 - Mendoza-Avila, Jesus A1 - Efimov, Denis A1 - Schiffer, Johannes T1 - Conditions for global synchronization in networks of heterogeneous Kuramoto oscillators T2 - Automatica N2 - 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. Y1 - 2025 U6 - https://doi.org/10.1016/j.automatica.2025.112180 SN - 0005-1098 VL - 175 SP - 1 EP - 11 PB - Elsevier BV CY - Amsterdam ER - TY - GEN A1 - Mendoza‐Avila, Jesus A1 - Efimov, Denis A1 - Angel Mercado‐Uribe, Jose A1 - Schiffer, Johannes T1 - Design of control laws for robust global stabilization of multistable state periodic systems T2 - International journal of robust and nonlinear control N2 - 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. KW - Global stabilization KW - Input-to-state stability KW - Multistability KW - Nonlinear control KW - Power systems KW - State periodic systems Y1 - 2025 U6 - https://doi.org/10.1002/rnc.70206 SN - 1049-8923 SN - 1099-1239 SP - 1 EP - 20 PB - Wiley CY - New York, NY ER -