Goodwill and Other Intangible Assets - Changes in Carrying amount of Goodwill (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Goodwill
Beginning balance	$ 3,524.0	$ 3,625.9
Acquisition of businesses	111.3	12.1
Goodwill impairment	(157.5)	0.0	$ 0.0
Translation and other	51.4	(114.0)
Ending balance	3,529.2	3,524.0	3,625.9
Gross carrying value of Goodwill	3,686.7
Accumulated impairment losses	(157.5)
Intelligent Devices
Goodwill
Beginning balance	503.0	543.1
Acquisition of businesses	74.4	0.0
Goodwill impairment	0.0
Translation and other	18.4	(40.1)
Ending balance	595.8	503.0	543.1
Gross carrying value of Goodwill	595.8
Accumulated impairment losses	0.0
Software & Control
Goodwill
Beginning balance	2,398.7	2,447.5
Acquisition of businesses	0.0	0.0
Goodwill impairment	0.0
Translation and other	21.4	(48.8)
Ending balance	2,420.1	2,398.7	2,447.5
Gross carrying value of Goodwill	2,420.1
Accumulated impairment losses	0.0
Lifecycle Services
Goodwill
Beginning balance	622.3	635.3
Acquisition of businesses	36.9	12.1
Goodwill impairment	(157.5)
Translation and other	11.6	(25.1)
Ending balance	513.3	$ 622.3	$ 635.3
Gross carrying value of Goodwill	670.8
Accumulated impairment losses	$ (157.5)