Business Segment Information - Components of Identifiable Assets, Depreciation and Amortization, and Capital Expenditures for Property (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019
Segment Reporting Information [Line Items]
Identifiable assets	$ 10,701.6	$ 7,264.7	$ 6,113.0
Depreciation and amortization	189.8	172.7	152.2
Purchase accounting depreciation and amortization	55.1	41.4	16.6
Capital expenditures	120.3	113.9	132.8
Corporate
Segment Reporting Information [Line Items]
Identifiable assets	2,433.6	2,692.0	2,557.0
Depreciation and amortization	1.7	1.8	2.2
Capital expenditures	18.3	18.4	6.5
Operating Segments
Segment Reporting Information [Line Items]
Depreciation and amortization	134.7	131.3	135.6
Intelligent Devices
Segment Reporting Information [Line Items]
Identifiable assets	2,143.3	1,585.0	1,550.0
Depreciation and amortization	48.6	51.8	56.0
Capital expenditures	52.0	51.3	74.8
Software & Control
Segment Reporting Information [Line Items]
Identifiable assets	4,000.4	1,072.7	872.7
Depreciation and amortization	49.1	40.6	42.6
Capital expenditures	30.4	19.3	34.8
Lifecycle Services
Segment Reporting Information [Line Items]
Identifiable assets	2,124.3	1,915.0	1,133.3
Depreciation and amortization	35.3	37.1	34.8
Capital expenditures	$ 19.6	$ 24.9	$ 16.7