On the commutative class of linear time-varying systems

Abstract
A new approach using the decomposition of A(t) to study the commutative class of linear time-varying systems is presented. A simpler and computer-implemental criterion of checking the commutativity of A(t) with its integral is given. More transparent results on solution, stability, decoupling, the controlability and observability are obtained. With the new approach, a commutative linear time-varying system can be studied in the same manner as that of a linear time-invariant system.

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