Singular Perturbation: When the Perturbation Parameter Becomes a State-Dependent Function

Tengfei Liu, Zhong Ping Jiang

Research output: Contribution to journalConference articlepeer-review


This paper introduces a new class of singularly perturbed systems in which the small, but constant, perturbation coefficient in standard singular perturbation theory is replaced by a state-dependent function. This generalization is aimed at broadening the applicability of singular perturbation theory in practice. For this class of singularly perturbed systems, it is assumed that the boundary-layer subsystem is globally asymptotically stable (GAS) at the origin and the reduced subsystem is input-to-state stable (ISS) with respect to the state of the boundary-layer subsystem. Under a mild monotonicity condition, sufficient conditions on the perturbation functions are given under which the singularly perturbed system is GAS at the origin. ISS and nonlinear small-gain techniques are exploited in the stability analysis. The efficacy of the proposed theoretical result is validated via its applications to tackling integral control and feedback optimization problems.

Original languageEnglish (US)
Pages (from-to)294-300
Number of pages7
Issue number1
StatePublished - Jan 1 2023
Event12th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2022 - Canberra, Australia
Duration: Jan 4 2023Jan 6 2023


  • Singular perturbation
  • global asymptotic stability
  • perturbation functions

ASJC Scopus subject areas

  • Control and Systems Engineering


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