Remarks on time-scale decomposition using singular perturbations with applications

Kliti Kodra, Ningfan Zhong, Zoran Gajic

Research output: Contribution to journalArticlepeer-review


In this paper, we point out important observations on time-scale decomposition of linear singularly perturbed systems. It has been established in the control literature that the asymptotically stable fast modes of a singularly perturbed system decay rapidly in a boundary layer interval when the perturbation parameter is very small hence the slow subsystem can serve as a good approximation of the original model. We observe that while this is the case in the steady state, it is not true during the transient response for a strictly proper system with highly damped and highly oscillatory modes. Instead, the fast subsystem provides a very good approximation of the original model’s response but with a DC gain offset. We propose a correction to rectify the DC gain offset and illustrate the findings using an islanded microgrid electric power system model.

Original languageEnglish (US)
Pages (from-to)538-552
Number of pages15
JournalAnnals of the Academy of Romanian Scientists: Series on Mathematics and its Applications
Issue number1-2
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


  • Islanded microgrid
  • Singular perturbations
  • Time-scale decomposition


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