Goodwill and Other Intangible Assets - Changes in Carrying amount of Goodwill (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2022	Sep. 30, 2021
Goodwill
Beginning balance	$ 3,625.9
Balance as of October 1, 2020		$ 1,650.3
Acquisition of businesses	12.1	1,950.1
Translation	(114.0)	25.5
Ending balance	3,524.0	3,625.9
Intelligent Devices
Goodwill
Beginning balance	543.1
Balance as of October 1, 2020		535.1
Acquisition of businesses	0.0	0.0
Translation	(40.1)	8.0
Ending balance	503.0	543.1
Software & Control
Goodwill
Beginning balance	2,447.5
Balance as of October 1, 2020		497.3
Acquisition of businesses	0.0	1,937.3
Translation	(48.8)	12.9
Ending balance	2,398.7	2,447.5
Lifecycle Services
Goodwill
Beginning balance	635.3
Balance as of October 1, 2020		617.9
Acquisition of businesses	12.1	12.8
Translation	(25.1)	4.6
Ending balance	$ 622.3	$ 635.3