Switching System Techniques for Linear Discrete-Time Systems

  • Dong ShenEmail author
  • Xuefang Li


This chapter proposes a convergence analysis of ILC for discrete-time linear systems with randomly iteration-varying lengths. No prior information is required on the probability distribution of randomly iteration-varying lengths. The conventional P-type update law is adopted with Arimoto-like gains and causal gains. The convergence both in almost sure and mean square senses is proved by direct mathematical calculations.


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    Schmid R (2007) Comments on “Robust optimal design and convergence properties analysis of iterative learning control approaches” and “On the P-type and Newton-type ILC schemes for dynamic systems with non-affine input factors”. Automatica 43(9):1666–1669MathSciNetCrossRefGoogle Scholar
  2. 2.
    Shen D, Zhang W, Wang Y, Chien C-J (2016) On almost sure and mean square convergence of P-type ilc under randomly varying iteration lengths. Automatica 63(1):359–365MathSciNetCrossRefGoogle Scholar

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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.College of Information Science and TechnologyBeijing University of Chemical TechnologyBeijingChina
  2. 2.Department of Electrical and Electronic EngineeringImperial College LondonLondonUK

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