COMMUTATIVITY OF HIGH-ORDER LINEAR TIME-VARYING SYSTEMS
Abstract
This paper presents the commutativity of high-order linear time-varying systems (LTVSs). Explicit conditions for the commutativity of high-order LTVSs are derived. The feedback conjugate pairs for high-order LTVSs are considered. The effects of sensitivity and disturbance on sixth-order LTVSs have been investigated. Example is given to support the results.
References
[1]E. Marshall, Commutativity of time-varying systems, Electro Lett. 18 (1977), 539 540.
[2]S. V. Saleh, Comments on ‘Commutativity of second-order time-varying systems’, International Journal of Control 37 (1983), 1195-1196.
[3]M. Koksal, General conditions for commutativity of time-varying systems, Telecommunication and Control (1984), 225-229.
[4]M. Koksal, Commutativity of 4th order systems and Euler systems time-varying systems, Proceedings of the National Congress of Electric Engineering, 1985, BI 6.
[5]M. E. Koksal and M. Koksal, Commutativity of linear time-varying differential systems with nonzero initial conditions: A Review. Mathematical Problems in Engineering (2011), 1-25.
[6]S. Ibrahim and M. E. Koksal, Commutativity of sixth-order time-varying linear systems, Circuits Syst. Signal Process. 40(10) (2021), 1-34. https://doi.org/10.1007/s00034-021-01709-6
[7]S. Ibrahim and M. E. Koksal, Realization of a fourth-order linear time-varying differential system with nonzero initial conditions by cascaded two second-order commutative pairs, Circuits Syst. Signal Process, 2021. https://doi.org/10.1007/s00034-020-01617-1
[8]S. Ibrahim and M. E. Koksal, Decomposition of fourth-order linear time-varying differential system into its twin second-order commutative pairs, 3rd International Symposium on Multidisciplinary Studies and Innovative Technologies, Ankara 2019, pp. 224-226.
[9]S. Ibrahim and M. E. Koksal, Decomposition of fourth-order linear time-varying system, 4th International Symposium on Innovative Approaches in Engineering and Natural Sciences, Samsun 4(6) (2019), pp. 139-141.
[10]S. Ibrahim, Explicit commutativity and stability for the Heun’s linear time- varying differential systems, Authorea 2021. https://doi.org/10.22541/au.162566323.35099726/v1
[11]S. Ibrahim and A. Rababah, Decomposition of fourth-order Euler-type linear time- varying differential systems, into Cascaded Two Second-Order Euler Commutative Pairs, Complexity, Vol. 2022, Article ID 3690019, 9 pages. https://doi.org/10.1155/2022/3690019