Necessary and sufficient conditions for the commutativity of linear time‐varying systems are
derived in the case of nonzero initial conditions. It is shown that some commutative class of …

This paper presents decomposition of the fourth‐order Euler‐type linear time‐varying
system (LTVS) as a commutative pair of two second‐order Euler‐type systems. All …

This paper studies commutativity of sixth-order differential systems with zero and nonzero
initial conditions (ICs). Given a sixth-order differential system A, we find its commutative pair …

Decomposition is an important tool that is used in many differential systems for solving real
engineering problems and improving the stability of a system. It involves breaking down of …

After introducing commutativity concept and summarizing the relevant literature, this work is
focused on the commutativity of feedback conjugates. It is already known that a linear time …

After summarizing the commutativity results for analogue linear time-varying systems, the
commutativity of cascade connected discrete-time linear time-varying systems is introduced …

The conditions for commutativity of two second-order time-varying systems presented
recently (Köksal 1982) are shown not to be necessary. Necessary and sufficient conditions …

Decomposition is a common tool for the synthesis of many physical systems. It is also used
for analyzing large-scale systems which are then known as tearing and reconstruction. On …

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 …

This paper, which is a survey and a compact reference on the commutativity of time-varying
systems, gives the complete set of necessary and sufficient commutativity conditions for …