Stable inversion of LPTV systems with application in position-dependent and non-equidistantly sampled systems

J.C.D van Zundert (Corresponding author), T.A.E. Oomen

Research output: Contribution to journalArticleAcademicpeer-review

6 Citations (Scopus)
91 Downloads (Pure)

Abstract

Many control applications, including feedforward and learning control, involve the inverse of a dynamical system. For nonminimum-phase systems, the response of the inverse system is unbounded. For linear time-invariant (LTI), nonminimum-phase systems, a bounded, noncausal inverse response can be obtained through an exponential dichotomy. For generic linear time-varying (LTV) systems, such a dichotomy does not exist in general. The aim of this paper is to develop an inversion approach for an important class of LTV systems, namely linear periodically time-varying (LPTV) systems, which occur in, e.g. position-dependent systems with periodic tasks and non-equidistantly sampled systems. The proposed methodology exploits the periodicity to determine a bounded inverse for general LPTV systems. Conditions for existence are provided. Themethod is successfully demonstrated in several application cases, including position-dependent and non-equidistantly sampled systems.
Original languageEnglish
Pages (from-to)1022-1032
Number of pages11
JournalInternational Journal of Control
Volume92
Issue number5
Early online date12 Oct 2017
DOIs
Publication statusPublished - 4 May 2019

Keywords

  • Stable inversion
  • dichotomy
  • linear periodically time-varying systems
  • linear time-varying systems
  • tracking control

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