TY - JOUR N2 - Although the explicit commutativitiy conditions for second-order linear time-varying systems have been appeared in some literature, these are all for initially relaxed systems. This paper presents explicit necessary and sufficient commutativity conditions for commutativity of second-order linear time-varying systems with non-zero initial conditions. It has appeared interesting that the second requirement for the commutativity of non-relaxed systems plays an important role on the commutativity conditions when non-zero initial conditions exist. Another highlight is that the commutativity of switched systems is considered and spoiling of commutativity at the switching instants is illustrated for the first time. The simulation results support the theory developed in the paper. L1 - http://journals.pan.pl/Content/113687/PDF/07_ACS-2019-3-INTERNET.pdf L2 - http://journals.pan.pl/Content/113687 PY - 2019 IS - No 3 EP - 529–548 DO - 10.24425/acs.2019.130204 KW - commutativity KW - linear systems KW - analogue control KW - robust control KW - differential equations KW - non-zero initial conditions A1 - Koksal, Mehmet Emir PB - Committee of Automatic Control and Robotics PAS VL - vol. 29 DA - 2019.09.23 T1 - Explicit commutativity conditions for second-order linear time-varying systems with non-zero initial conditions SP - 529–548 UR - http://journals.pan.pl/dlibra/publication/edition/113687 T2 - Archives of Control Sciences ER -