Goodwill and Other Intangible Assets - Changes in Carrying Amount of Goodwill (Details) $ in Millions	6 Months Ended
Mar. 31, 2021 USD ($)
Goodwill
Balance at beginning of period	$ 1,650.3
Reallocation due to change in Segments	0.0
Acquisition of businesses	219.8
Translation	24.9
Balance at end of period	1,895.0
Architecture & Software
Goodwill
Balance at beginning of period	609.4
Reallocation due to change in Segments	(609.4)
Acquisition of businesses	0.0
Translation	0.0
Balance at end of period	0.0
Control Products & Solutions
Goodwill
Balance at beginning of period	1,040.9
Reallocation due to change in Segments	(1,040.9)
Acquisition of businesses	0.0
Translation	0.0
Balance at end of period	0.0
Intelligent Devices
Goodwill
Balance at beginning of period	0.0
Reallocation due to change in Segments	535.1
Acquisition of businesses	0.0
Translation	8.0
Balance at end of period	543.1
Software & Control
Goodwill
Balance at beginning of period	0.0
Reallocation due to change in Segments	497.3
Acquisition of businesses	207.0
Translation	12.2
Balance at end of period	716.5
Lifecycle Services
Goodwill
Balance at beginning of period	0.0
Reallocation due to change in Segments	617.9
Acquisition of businesses	12.8
Translation	4.7
Balance at end of period	$ 635.4

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

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
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-Subparagraph (SX 210.9-03(10)(1))
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-Topic 350
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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.

+ References

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-Publisher FASB
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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.

+ References

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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.

+ References

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