Decomposition of 4 th -Order Bessel-type LTVS into Series Connection of two 2 nd -Order Bessel Commutative Pairs

A successive technique for decomposition of the 4 th -order linear time-varying system (LTVS) is employed to study the reduction process of 4-order Bessel-type LTVS into the series connection of two 2-order Bessel-type LTVSs. The general theories for decomposition and commutativity are derived alongside the sensitivity and effect due to disturbance that might arise on the 4 th -order Bessel-type LTVS. The derived theorems and example are proven and solved respectively to tackle the complexity of commutativity and the decomposition process which is useful for industrial and design practitioners. Moreover, the simulation and the theoretical results obtained are in good agreement with each other. Furthermore, the Bessel systems have constant forward feedback conjugates and non-constant feedback conjugates which are commutative pairs. However, there can be no doubt that the novelty is ensured since the current study is the very first to propose the decomposition of 4th-order Bessel-type LTVS as a commutative two 2nd -order Bessel-type systems.