Business Segment Information - Identifiable Assets (Details) - USD ($) $ in Millions	Dec. 31, 2020	Sep. 30, 2020	Sep. 30, 2019
Segment Reporting Information [Line Items]
Assets	$ 8,171.0	$ 7,264.7	$ 7,264.7
Corporate
Segment Reporting Information [Line Items]
Assets	3,147.4		2,692.0
Intelligent Devices | Operating Segments
Segment Reporting Information [Line Items]
Assets	1,679.5		1,585.0
Software & Control | Operating Segments
Segment Reporting Information [Line Items]
Assets	1,441.3		1,072.7
Lifecycle Services | Operating Segments
Segment Reporting Information [Line Items]
Assets	$ 1,902.8		$ 1,915.0