Business Segment Information - Components of Identifiable Assets, Depreciation and Amortization, and Capital Expenditures for Property (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Segment Reporting Information [Line Items]
Identifiable assets	$ 11,232.1	$ 11,304.0	$ 10,758.7
Depreciation and amortization	317.4	250.4	238.9
Purchase accounting depreciation and amortization	143.9	106.9	103.9
Capital expenditures for property	224.7	160.5	141.1
Operating Segments
Segment Reporting Information [Line Items]
Depreciation and amortization	173.5	143.5	135.0
Corporate
Segment Reporting Information [Line Items]
Identifiable assets	2,104.7	2,551.3	2,832.7
Depreciation and amortization	4.2	2.5	1.7
Capital expenditures for property	29.6	35.9	32.9
Intelligent Devices | Operating Segments
Segment Reporting Information [Line Items]
Identifiable assets	2,798.1	2,676.2	2,070.0
Depreciation and amortization	57.7	49.7	45.8
Capital expenditures for property	74.9	60.7	45.6
Software & Control | Operating Segments
Segment Reporting Information [Line Items]
Identifiable assets	4,293.0	4,240.7	3,887.6
Depreciation and amortization	68.4	55.8	47.0
Capital expenditures for property	67.5	40.2	29.7
Lifecycle Services | Operating Segments
Segment Reporting Information [Line Items]
Identifiable assets	2,036.3	1,835.8	1,968.4
Depreciation and amortization	43.2	35.5	40.5
Capital expenditures for property	$ 52.7	$ 23.7	$ 32.9