Decomposition of a second-order linear time-varying differential system as the series connection of two first order commutative pairs

Köksal M. E.

OPEN MATHEMATICS, vol.14, pp.693-704, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14
  • Publication Date: 2016
  • Doi Number: 10.1515/math-2016-0059
  • Journal Name: OPEN MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.693-704
  • Keywords: Differential equations, Analogue control, Equivalent circuits, Feedback circuits, Feedback control systems, Robust control, CASCADE CONNECTION, STABILITY
  • Ondokuz Mayıs University Affiliated: Yes


Necessary and sufficiently conditions are derived for the decomposition of a second order linear time-varying system into two cascade connected commutative first order linear time-varying subsystems. The explicit formulas describing these subsystems are presented. It is shown that a very small class of systems satisfies the stated conditions. The results are well verified by simulations. It is also shown that its cascade synthesis is less sensitive to numerical errors than the direct simulation of the system itself.