TY - GEN A1 - Schiffer, Johannes A1 - Barabanov, Nikita A1 - Ortega, Romeo A1 - Efimov, Denis T1 - Conditions for Almost Global Attractivity of a Synchronous Generator Connected to an Infinite Bus T2 - Transactions on Automatic Control N2 - Conditions for existence and global attractivity of the equilibria of a realistic model of a synchronous generator with constant field current connected to an infinite bus are derived. First, necessary and sufficient conditions for existence and uniqueness of equilibrium points are provided. Then, sufficient conditions for local asymptotic stability and almost global attractivity of one of these equilibria are given. The analysis is carried out by employing a new Lyapunov-like function to establish convergence of bounded trajectories, while the latter is proven using the powerful theoretical framework of cell structures pioneered by Leonov and Noldus. The efficiency of the derived sufficient conditions is illustrated via extensive numerical experiments based on two benchmark examples taken from the literature. Y1 - 2017 UR - https://ieeexplore.ieee.org/document/7858643 U6 - https://doi.org/10.1109/TAC.2017.2671026 SN - 1558-2523 SN - 0018-9286 VL - 62 IS - 10 SP - 4905 EP - 4916 ER - TY - GEN A1 - Schiffer, Johannes A1 - Efimov, Denis A1 - Ortega, Romeo A1 - Barabanov, Nikita T1 - An Input-to-State Stability Approach to Verify Almost Global Stability of a Synchronous-Machine-Infinite-Bus System T2 - Philosophical transactions of the Royal Society. Series A, Mathematical, physical and engineering sciences N2 - Conditions for almost global stability of an operating point of a realistic model of a synchronous generator with constant field current connected to an infinite bus are derived. The analysis is conducted by employing the recently proposed concept of input-to-state stability (ISS)–Leonov functions, which is an extension of the powerful cell structure principle developed by Leonov and Noldus to the ISS framework. Compared with the original ideas of Leonov and Noldus, the ISS–Leonov approach has the advantage of providing additional robustness guarantees. The efficiency of the derived sufficient conditions is illustrated via numerical experiments. Y1 - 2017 U6 - https://doi.org/10.1098/rsta.2016.0304 SN - 1364-503X SN - 1471-2962 VL - 375 IS - 2100 ER - TY - GEN A1 - Schiffer, Johannes A1 - Efimov, Denis A1 - Barabanov, Nikita A1 - Ortega, Romeo T1 - Relaxing the Conditions of ISS for Multistable Periodic Systems T2 - IFAC-PapersOnLine N2 - The input-to-state stability property of nonlinear dynamical systems with multiple invariant solutions is analyzed under the assumption that the system equations are periodic with respect to certain state variables. It is shown that stability can be concluded via a sign-indefinite function, which explicitly takes the systems' periodicity into account. The presented approach leverages some of the difficulties encountered in the analysis of periodic systems via positive definite Lyapunov functions proposed in Angeli and Efimov (2013, 2015). The new result is established based on the framework of cell structure introduced in Leonov (1974) and illustrated via the global analysis of a nonlinear pendulum with a constant persistent input. Y1 - 2017 UR - https://hal.inria.fr/hal-01508766 U6 - https://doi.org/10.1016/j.ifacol.2017.08.1365 VL - 50 IS - 1 SP - 7217 EP - 7222 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 - TY - GEN A1 - Rueda-Escobedo, Juan G. A1 - Ushirobira, Rosane A1 - Efimov, Denis A1 - Moreno, Jaime A. T1 - Gramian-based uniform convergent observer for stable LTV systems with delayed measurements T2 - International Journal of Control Volume N2 - In this work, an observer for a linear time-varying system with delayed measurements is developed. The delay is assumed to be unknown, bounded, and it can be time-varying with no restriction on its rate of change. The observer uses auxiliary signals related to the constructibility Gramian of the system and it contains nonlinearities that provide a uniform fixed-time convergence to a bounded region in the estimation error coordinates. This means that the convergence time can be bounded by a positive constant which is independent from the initial conditions and the initial time. This property is new for the addressed class of systems. The ultimate bound of the estimation error depends on the maximum difference between the nominal output and the delayed one, and not directly on the delay size or its time derivative. These properties are illustrated in a numerical simulation. Y1 - 2020 U6 - https://doi.org/10.1080/00207179.2019.1569256 SN - 0020-7179 SN - 1366-5820 VL - 93 IS - 2 SP - 226 EP - 237 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 - 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 - 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 - 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 - On Relaxed Conditions of Integral ISS for Multistable Periodic Systems T2 - Proceedings of the 2021 61st IEEE Conference on Decision and Control (CDC) N2 - 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. Y1 - 2022 UR - https://hal.archives-ouvertes.fr/hal-03778051/ ER -