ISS of multistable systems with delays: application to droop-controlled inverter-based microgrids

Denis Efimov 1 Romeo Ortega 2 Johannes Schiffer 3
1 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : Motivated by the problem of phase-locking in droop-controlled inverter-based microgrids with delays, the recently developed theory of input-to-state stability (ISS) for multistable systems is extended to the case of multistable systems with delayed dynamics. Sufficient conditions for ISS of delayed systems are presented using Lyapunov-Razumikhin functions. It is shown that ISS multistable systems are robust with respect to delays in a feedback. The derived theory is applied to two examples. First, the ISS property is established for the model of a nonlinear pendulum and delay-dependent ro-bustness conditions are derived. Second, it is shown that, under certain assumptions, the problem of phase-locking analysis in droop-controlled inverter-based microgrids with delays can be reduced to the stability investigation of the nonlinear pendulum. For this case, corresponding delay-dependent conditions for asymptotic phase-locking are given.
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Denis Efimov, Romeo Ortega, Johannes Schiffer. ISS of multistable systems with delays: application to droop-controlled inverter-based microgrids. 2015 American Control Conference (ACC), Jul 2015, Chicago, United States. ⟨10.1109/acc.2015.7172064 ⟩. ⟨hal-01140346⟩

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