Goodwill and Other Intangible Assets - Changes in Carrying amount of Goodwill (Details) - USD ($) $ in Millions	12 Months Ended
Sep. 30, 2021	Sep. 30, 2020
Goodwill
Beginning balance	$ 1,650.3	$ 1,071.1
Acquisition of businesses	1,950.1	551.9
Translation	25.5	27.3
Reallocation due to change in segments	0.0
Ending balance	3,625.9	1,650.3
Architecture & Software
Goodwill
Beginning balance	609.4	432.3
Acquisition of businesses		161.2
Translation		15.9
Reallocation due to change in segments	(609.4)
Ending balance	0.0	609.4
Control Products & Solutions
Goodwill
Beginning balance	1,040.9	638.8
Acquisition of businesses		390.7
Translation		11.4
Reallocation due to change in segments	(1,040.9)
Ending balance	0.0	$ 1,040.9
Intelligent Devices
Goodwill
Translation	8.0
Reallocation due to change in segments	535.1
Ending balance	543.1
Software & Control
Goodwill
Acquisition of businesses	1,937.3
Translation	12.9
Reallocation due to change in segments	497.3
Ending balance	2,447.5
Lifecycle Services
Goodwill
Acquisition of businesses	12.8
Translation	4.6
Reallocation due to change in segments	617.9
Ending balance	$ 635.3

Goodwill, Change in Goodwill Allocation

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- Definition

Amount after accumulated impairment loss of an asset representing future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized.

+ References

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- Definition

Amount of increase in asset representing future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized resulting from a business combination.

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- Definition

Amount of foreign currency translation gain (loss) which increases (decreases) an asset representing future economic benefits from other assets acquired in a business combination that are not individually identified and separately recognized.

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- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

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