Goodwill and Other Intangible Assets - Changes in Carrying Amount of Goodwill (Details) $ in Millions	9 Months Ended
	Jun. 30, 2021 USD ($)
Goodwill
Balance at beginning of period	$ 1,650.3
Reallocation due to change in Segments	0.0
Acquisition of businesses	224.8
Translation	40.9
Balance at end of period	1,916.0
Architecture & Software
Goodwill
Balance at beginning of period	609.4
Reallocation due to change in Segments	(609.4)
Acquisition of businesses	0.0
Translation	0.0
Balance at end of period	0.0
Control Products & Solutions
Goodwill
Balance at beginning of period	1,040.9
Reallocation due to change in Segments	(1,040.9)
Acquisition of businesses	0.0
Translation	0.0
Balance at end of period	0.0
Intelligent Devices
Goodwill
Balance at beginning of period	0.0
Reallocation due to change in Segments	535.1
Acquisition of businesses	0.0
Translation	15.3
Balance at end of period	550.4
Software & Control
Goodwill
Balance at beginning of period	0.0
Reallocation due to change in Segments	497.3
Acquisition of businesses	212.0
Translation	16.8
Balance at end of period	726.1
Lifecycle Services
Goodwill
Balance at beginning of period	0.0
Reallocation due to change in Segments	617.9
Acquisition of businesses	12.8
Translation	8.8
Balance at end of period	$ 639.5