Transitivity of Commutativity for Linear Time-Varying Physical Systems

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.