@misc{SchifferEfimov, author = {Schiffer, Johannes and Efimov, Denis}, title = {A new criterion for boundedness of solutions for a class of periodic systems}, series = {17th European Control Conference (ECC), Limassol, Cyprus, 2018}, journal = {17th European Control Conference (ECC), Limassol, Cyprus, 2018}, pages = {6}, language = {en} } @misc{SchifferEfimovOrtega, author = {Schiffer, Johannes and Efimov, Denis and Ortega, Romeo}, title = {Almost Global Synchronization in Multi-Machine Power Systems}, series = {57th IEEE Conference on Decision and Control, Miami Beach, FL, USA, December 17-19, 2018}, journal = {57th IEEE Conference on Decision and Control, Miami Beach, FL, USA, December 17-19, 2018}, publisher = {IEEE}, address = {Piscataway, NJ}, isbn = {978-1-5386-1395-5}, doi = {10.1109/CDC.2018.8619788}, pages = {800 -- 805}, language = {en} } @misc{SchifferEfimovBarabanovetal., author = {Schiffer, Johannes and Efimov, Denis and Barabanov, Nikita and Ortega, Romeo}, title = {A Relaxed Characterization of ISS for Periodic Systems with Multiple Invariant Sets}, series = {European Journal of Control}, volume = {Vol. 37}, journal = {European Journal of Control}, issn = {1435-5671}, doi = {10.1016/j.ejcon.2017.04.002}, pages = {1 -- 7}, abstract = {A necessary and sufficient criterion to establish input-to-state stability (ISS) of nonlinear dynamical systems, the dynamics of which are periodic with respect to certain state variables and which possess multiple invariant solutions (equilibria, limit cycles, etc.), is provided. Unlike standard Lyapunov approaches, the condition is relaxed and formulated via a sign-indefinite function with sign-definite derivative, and by taking the system's periodicity explicitly into account. The new result is established by using the framework of cell structure and it complements the ISS theory of multistable dynamics for periodic systems. The efficiency of the proposed approach is illustrated via the global analysis of a nonlinear pendulum with constant persistent input.}, language = {en} } @misc{SchifferBarabanovOrtegaetal., author = {Schiffer, Johannes and Barabanov, Nikita and Ortega, Romeo and Efimov, Denis}, title = {Conditions for Almost Global Attractivity of a Synchronous Generator Connected to an Infinite Bus}, series = {Transactions on Automatic Control}, volume = {62}, journal = {Transactions on Automatic Control}, number = {10}, issn = {1558-2523}, doi = {10.1109/TAC.2017.2671026}, pages = {4905 -- 4916}, abstract = {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.}, language = {en} } @misc{SchifferEfimovOrtegaetal., author = {Schiffer, Johannes and Efimov, Denis and Ortega, Romeo and Barabanov, Nikita}, title = {An Input-to-State Stability Approach to Verify Almost Global Stability of a Synchronous-Machine-Infinite-Bus System}, series = {Philosophical transactions of the Royal Society. Series A, Mathematical, physical and engineering sciences}, volume = {375}, journal = {Philosophical transactions of the Royal Society. Series A, Mathematical, physical and engineering sciences}, number = {2100}, issn = {1364-503X}, doi = {10.1098/rsta.2016.0304}, abstract = {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.}, language = {en} } @misc{SchifferEfimovBarabanovetal., author = {Schiffer, Johannes and Efimov, Denis and Barabanov, Nikita and Ortega, Romeo}, title = {Relaxing the Conditions of ISS for Multistable Periodic Systems}, series = {IFAC-PapersOnLine}, volume = {50}, journal = {IFAC-PapersOnLine}, number = {1}, doi = {10.1016/j.ifacol.2017.08.1365}, pages = {7217 -- 7222}, abstract = {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.}, language = {en} } @misc{SchifferEfimovOrtega, author = {Schiffer, Johannes and Efimov, Denis and Ortega, Romeo}, title = {Global synchronization analysis of droop-controlled microgrids—A multivariable cell structure approach}, series = {Automatica}, journal = {Automatica}, number = {109}, issn = {0005-1098}, doi = {10.1016/j.automatica.2019.108550}, pages = {12}, abstract = {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.}, language = {en} } @misc{EfimovSchiffer, author = {Efimov, Denis and Schiffer, Johannes}, title = {On boundedness of solutions of state periodic systems: a multivariable cell structure approach}, series = {IEEE Transactions on Automatic Control}, volume = {64}, journal = {IEEE Transactions on Automatic Control}, number = {10}, issn = {0018-9286}, doi = {10.1109/TAC.2019.2892395}, pages = {4094 -- 4104}, abstract = {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.}, language = {en} } @misc{RuedaEscobedoUshirobiraEfimovetal., author = {Rueda-Escobedo, Juan G. and Ushirobira, Rosane and Efimov, Denis and Moreno, Jaime A.}, title = {Gramian-based uniform convergent observer for stable LTV systems with delayed measurements}, series = {International Journal of Control Volume}, volume = {93}, journal = {International Journal of Control Volume}, number = {2}, issn = {0020-7179}, doi = {10.1080/00207179.2019.1569256}, pages = {226 -- 237}, abstract = {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.}, language = {en} } @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{SchifferEfimov, author = {Schiffer, Johannes and Efimov, Denis}, title = {Strong and Weak Leonov Functions for Global Boundedness of State Periodic Systems}, series = {IEEE Transactions on Automatic Control}, volume = {68}, journal = {IEEE Transactions on Automatic Control}, number = {12}, issn = {0018-9286}, doi = {10.1109/TAC.2023.3251903}, pages = {7958 -- 7965}, abstract = {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.}, 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} }