Business Segment Information - Components of Identifiable Assets, Depreciation and Amortization, and Capital Expenditures for Property (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Segment Reporting Information [Line Items]
Identifiable assets	$ 11,304.0	$ 10,758.7	$ 10,701.6
Depreciation and amortization	250.4	238.9	189.8
Purchase accounting depreciation and amortization	106.9	103.9	55.1
Impairment	157.5	0.0	0.0
Capital expenditures	160.5	141.1	120.3
Operating Segments
Segment Reporting Information [Line Items]
Depreciation and amortization	143.5	135.0	134.7
Corporate
Segment Reporting Information [Line Items]
Identifiable assets	2,551.3	2,832.7	2,433.6
Depreciation and amortization	2.5	1.7	1.7
Capital expenditures	35.9	32.9	18.3
Intelligent Devices
Segment Reporting Information [Line Items]
Impairment	0.0
Intelligent Devices | Operating Segments
Segment Reporting Information [Line Items]
Identifiable assets	2,676.2	2,070.0	2,143.3
Depreciation and amortization	49.7	45.8	48.6
Capital expenditures	60.7	45.6	52.0
Software & Control
Segment Reporting Information [Line Items]
Impairment	0.0
Software & Control | Operating Segments
Segment Reporting Information [Line Items]
Identifiable assets	4,240.7	3,887.6	4,000.4
Depreciation and amortization	55.8	47.0	49.1
Capital expenditures	40.2	29.7	30.4
Lifecycle Services | Operating Segments
Segment Reporting Information [Line Items]
Identifiable assets	1,835.8	1,968.4	2,124.3
Depreciation and amortization	35.5	40.5	35.3
Capital expenditures	$ 23.7	$ 32.9	$ 19.6