After summarizing the commutativity results for analogue linear time-varying systems, the commutativity of cascade connected discrete-time linear time-varying systems is introduced. Some general open questions on the subject are stated and new results are presented, intended to answer some of them. Two examples are given to reinforce the concept and to show up its possible benefits in engineering to reduce noise effects and design robust systems.
DorfRCSvadovaJA (2004) Introduction to Electric Circuits. New York: Wiley.
3.
HykinS (1988) Digital Communucation. New York: Wiley.
4.
KoksalM (1982a) Commutativity of second order time-varying systems. In: Proceedings of the 6th Summer Symposium on Circuit Theory, Prague, Czechoslavakia, pp. 305–309.
5.
KoksalM (1982b) Commutativity of low order time-varying systems. In: Proceedings of the 7th Colloquium on Microwave Communication, Budapest, Hungary, pp. 230–231.
6.
KoksalM (1982c) Commutativity of second order time-varying systems. International Journal of Control3: 541–544.
7.
KoksalM (1983) Corrections on Commutativity of second order time-varying systems. International Journal of Control1: 273–274.
8.
KoksalM (1984) General conditions for commutativity of time-varying systems. In: Proceedings of IASTED International conference on Telecommunication and Control, Halkidiki, Greece, pp. 229–225.
9.
KoksalM (1985a) A survey on the commutativity of time-varying systems. METU, Gaziantep Electrical-Electronics Engineering Department, Circuits and Systems, Technical Report no: GEEE/CAS-85/1.
10.
KoksalM (1985b) Commutativity of 4th order systems and Euler systems. National Congress of Electrical Engineers, Adana, Turkey, pp. BI–6.
11.
KoksalM (1987) Effects of initial conditions on the commutativity and effects of commutativity on the system sensitivity. In: Proceedings of 2nd National Congress of Electrical Engineers, Ankara, Turkey, pp. 570–573.
12.
KoksalM (1988a) An exhaustive study on the commutativity of time-varying systems. International Journal of Control5: 1521–1537.
13.
KoksalM (1988b) Effects of nonzero initial conditions on the commutativity of linear time-varying systems. In: Proceedings of International AMSE Conference on Modelling and Simulation, Istanbul, Turkey, pp. 49–55.
14.
KoksalM (1989) Effects of commutativity on system sensitivity. In: Proceedings of 6th International Symposium on Networks, Systems and Signal Processing, Zagrep, Yugoslavia, pp. 61–62.
15.
KoksalMKoksalME (2011) Commutativity of linear time-varying differential systems with non-zero initial conditions: a review and some new extensions. Mathematical Problems in Engineering2011: 1–25.
16.
KoksalMEKoksalM (2013) Commutativity of cascade connected discrete time linear time-varying systems. In: Proceedings of the 2013 Automatic Control National Meeting TOK’2013, Malatya, Turkey, pp. 1128–1131.
17.
MarshallE (1977) Commutativity of time varying systems. Electronic Letters18: 539–540.
18.
MillerGMBeasleyJS (2002) Modern Electronic Communication. Englewood Cliffs, NJ: Prentice Hall.
19.
SalehSV (1983) Comments on Commutativity of second-order time-varying systems. International Journal of Control37: 1195–1195.
20.
SkalarB (2001) Digital Communications: Fundamentals and Applications. Englewood Cliffs, NJ: Prentice Hall.
21.
YoungPH (1994) Electronic Communication TechniquesEnglewood Cliffs, NJ: Prentice Hall.
