Robustness of delayed multistable systems with application to droop-controlled inverter-based microgrids

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 robustness 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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International Journal of Control, Taylor & Francis, 2016, 89 (5), pp.909-918. 〈10.1080/00207179.2015.1104555〉
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Denis Efimov, Johannes Schiffer, Romeo Ortega. Robustness of delayed multistable systems with application to droop-controlled inverter-based microgrids. International Journal of Control, Taylor & Francis, 2016, 89 (5), pp.909-918. 〈10.1080/00207179.2015.1104555〉. 〈hal-01211454〉

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