Goodwill and Other Intangible Assets - Changes in Carrying Amount of Goodwill (Details) $ in Millions	3 Months Ended
	Dec. 31, 2023 USD ($)
Goodwill
Balance at beginning of period	$ 3,529.2
Acquisition of businesses	400.0
Translation	37.5
Balance at end of period	3,966.7
Gross carrying value of goodwill	4,124.2
Accumulated impairment losses	(157.5)
Intelligent Devices
Goodwill
Balance at beginning of period	595.8
Acquisition of businesses	267.0
Translation	16.9
Balance at end of period	879.7
Gross carrying value of goodwill	879.7
Accumulated impairment losses	0.0
Software & Control
Goodwill
Balance at beginning of period	2,420.1
Acquisition of businesses	0.0
Translation	13.5
Balance at end of period	2,433.6
Gross carrying value of goodwill	2,433.6
Accumulated impairment losses	0.0
Lifecycle Services
Goodwill
Balance at beginning of period	513.3
Acquisition of businesses	133.0
Translation	7.1
Balance at end of period	653.4
Gross carrying value of goodwill	810.9
Accumulated impairment losses	$ (157.5)