Business Segment Information - Components of Identifiable Assets, Depreciation and Amortization, and Capital Expenditures for Property (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2020
Segment Reporting Information [Line Items]
Identifiable assets	$ 10,758.7	$ 10,701.6	$ 7,264.7
Depreciation and amortization	238.9	189.8	172.7
Purchase accounting depreciation and amortization	103.9	55.1	41.4
Capital expenditures	141.1	120.3	113.9
Operating Segments
Segment Reporting Information [Line Items]
Depreciation and amortization	135.0	134.7	131.3
Corporate
Segment Reporting Information [Line Items]
Identifiable assets	2,832.7	2,433.6	2,692.0
Depreciation and amortization	1.7	1.7	1.8
Capital expenditures	32.9	18.3	18.4
Intelligent Devices | Operating Segments
Segment Reporting Information [Line Items]
Identifiable assets	2,070.0	2,143.3	1,585.0
Depreciation and amortization	45.8	48.6	51.8
Capital expenditures	45.6	52.0	51.3
Software & Control | Operating Segments
Segment Reporting Information [Line Items]
Identifiable assets	3,887.6	4,000.4	1,072.7
Depreciation and amortization	47.0	49.1	40.6
Capital expenditures	29.7	30.4	19.3
Lifecycle Services | Operating Segments
Segment Reporting Information [Line Items]
Identifiable assets	1,968.4	2,124.3	1,915.0
Depreciation and amortization	40.5	35.3	37.1
Capital expenditures	$ 32.9	$ 19.6	$ 24.9