Goodwill and Other Intangible Assets - Changes in Carrying Amount of Goodwill (Details) $ in Millions	9 Months Ended
	Jun. 30, 2024 USD ($)
Goodwill
Balance at beginning of period	$ 3,529.2
Acquisition of businesses	416.3
Translation	8.2
Balance at end of period	3,953.7
Gross carrying value of goodwill	4,111.2
Accumulated impairment losses	(157.5)
Intelligent Devices
Goodwill
Balance at beginning of period	595.8
Acquisition of businesses	282.8
Translation	3.7
Balance at end of period	882.3
Gross carrying value of goodwill	882.3
Accumulated impairment losses	0.0
Software & Control
Goodwill
Balance at beginning of period	2,420.1
Acquisition of businesses	0.0
Translation	2.9
Balance at end of period	2,423.0
Gross carrying value of goodwill	2,423.0
Accumulated impairment losses	0.0
Lifecycle Services
Goodwill
Balance at beginning of period	513.3
Acquisition of businesses	133.5
Translation	1.6
Balance at end of period	648.4
Gross carrying value of goodwill	805.9
Accumulated impairment losses	$ (157.5)