Decomposition of Fourth-Order Linear Time-Varying Systems into its Third- and First-Order Commutative Pairs

Ibrahim S., Köksal M. E.

CIRCUITS SYSTEMS AND SIGNAL PROCESSING, vol.42, pp.3320-3340, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42
  • Publication Date: 2023
  • Doi Number: 10.1007/s00034-022-02272-4
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Communication Abstracts, Compendex, zbMATH
  • Page Numbers: pp.3320-3340
  • Keywords: Analog control, Robust control, Time-varying linear system, Differential equation, Physical systems, CASCADE CONNECTION, 2ND
  • Ondokuz Mayıs University Affiliated: Yes


The necessary and sufficient conditions for decomposing a fourth-order (FO) linear time-variant system (LTVS) in the form of cascade connection of a first-order system and a third-order system that are commutative are expressed explicitly in this paper. Some additional conditions are also derived for a valid decomposition when the initial conditions are different from zero. Further, explicit formulas are derived for the determination of the decomposed subsystems. The paper also investigated the effects of changing the connection order on the sensitivity and disturbance properties. Theoretical results about the decomposition are supported and illustrated by considering various examples.