Transitivity of Commutativity for Linear Time-Varying Physical Systems

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Köksal M. E.

JOURNAL OF ELECTRICAL ENGINEERING & TECHNOLOGY, vol.16, no.2, pp.1071-1082, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.1007/s42835-020-00609-0
  • Journal Name: JOURNAL OF ELECTRICAL ENGINEERING & TECHNOLOGY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC
  • Page Numbers: pp.1071-1082
  • Keywords: Commutativity, Time-varying systems, Linear systems, Differential equations, Impulse response, NONLINEAR-SYSTEMS
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this contribution, the transitivity property of commutative first-order linear time-varying systems with and without initial conditions is investigated. It is proven that transitivity property of first-order systems holds with and without initial conditions. On the base of impulse response function, transitivity of commutation property is formulated for any triplet of commutative linear time-varying relaxed systems. Transitivity proves are given for some special combinations of first and second-order linear time-varying systems which are initially relaxed.