Periodic Averaging of Discrete-Time Systems: A Time-Delay Approach

Xuefei Yang, Jin Zhang, Emilia Fridman

Research output: Contribution to journalArticlepeer-review


This article is concerned with the stability of discrete-time systems with fast-varying coefficients that may be uncertain. Recently, a constructive time-delay approach to averaging was proposed for continuous-time systems. In the present article, we develop, for the first time, this approach to discrete-time case. We first transform the system to a time-delay system with the delay being the period of averaging, which can be regarded as a perturbation of the classical averaged system. The stability of the original system can be guaranteed by the resulting time-delay system. Then under assumption of the classical averaged system being exponentially stable, we derive sufficient stability conditions for the resulting time-delay system, and find a quantitative upper bound on the small parameter that ensures the exponential stability. Moreover, we extend our method to input-to-state stability (ISS) analysis of the perturbed systems. Finally, we apply the approach to the practical stability of discrete-time switched affine systems, where an explicit ultimate bound in terms of the switching period is presented. Two numerical examples are given to illustrate the efficiency of results.

Original languageEnglish
Pages (from-to)1-8
Number of pages8
JournalIEEE Transactions on Automatic Control
StateAccepted/In press - 2022


  • Averaging
  • Discrete-time systems
  • ISS
  • Linear matrix inequalities
  • Numerical stability
  • Stability criteria
  • Switches
  • Uncertainty
  • Upper bound
  • discrete-time systems
  • switched affine systems
  • time-delay systems


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