Advances in Differential Equations and Control Processes

The Advances in Differential Equations and Control Processes is an esteemed international journal indexed in the Emerging Sources Citation Index (ESCI). It publishes original research articles related to recent developments in both theory and applications of ordinary and partial differential equations, integral equations, and control theory. The journal highlights the interdisciplinary nature of these topics, with applications in physical, biological, environmental, and health sciences, mechanics, and engineering. It also considers survey articles that identify future avenues of advancement in the field.

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COMMUTATIVITY OF HIGH-ORDER LINEAR TIME-VARYING SYSTEMS

Authors

  • Salisu Ibrahim

Keywords:

commutativity, linear time-varying systems and analogue control.

DOI:

https://doi.org/10.17654/0974324322013

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.

Received: January 24, 2022
Accepted: March 15, 2022

References

E. Marshall, Commutativity of time-varying systems, Electro Lett. 18 (1977), 539 540.

S. V. Saleh, Comments on ‘Commutativity of second-order time-varying systems’, International Journal of Control 37 (1983), 1195-1196.

M. Koksal, General conditions for commutativity of time-varying systems, Telecommunication and Control (1984), 225-229.

M. Koksal, Commutativity of 4th order systems and Euler systems time-varying systems, Proceedings of the National Congress of Electric Engineering, 1985, BI 6.

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.

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

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

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.

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.

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

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

Published

2022-03-26

Issue

Section

Articles

How to Cite

COMMUTATIVITY OF HIGH-ORDER LINEAR TIME-VARYING SYSTEMS. (2022). Advances in Differential Equations and Control Processes, 27, 73-83. https://doi.org/10.17654/0974324322013

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