TY - JOUR A2 - Liatsis, P. AU - Koksal, Muhammet AU - Koksal, Mehmet Emir PY - 2011 DA - 2011/10/10 TI - Commutativity of Linear Time-Varying Differential Systems with Nonzero Initial Conditions: A Review and Some New Extensions SP - 678575 VL - 2011 AB - 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 linear time-varying systems may not commute with arbitrary initial conditions. In this respect, commutativity of Euler differential systems is investigated. Explicit commutativity conditions for the fifth-order systems are solved. New results about the effects of commutativity on system sensitivity and disturbance properties are presented, which is very important for network design and industrial applications where many of the systems are composed of subsystems cooperating one after another in a chain. The results are supported by examples treated either analytically or numerically. SN - 1024-123X UR - https://doi.org/10.1155/2011/678575 DO - 10.1155/2011/678575 JF - Mathematical Problems in Engineering PB - Hindawi Publishing Corporation KW - ER -