Business Segment Information - Components of Identifiable Assets, Depreciation and Amortization, and Capital Expenditures for Property (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2018
Segment Reporting Information [Line Items]
Identifiable assets	$ 7,264.7	$ 6,113.0	$ 6,262.0
Depreciation and amortization	172.7	152.2	164.6
Purchase accounting depreciation and amortization	41.4	16.6	17.4
Capital expenditures	113.9	132.8	125.5
Corporate
Segment Reporting Information [Line Items]
Identifiable assets	2,680.1	2,587.7	2,378.2
Depreciation and amortization	1.8	2.2	2.3
Capital expenditures	19.0	6.2	57.6
Operating Segments
Segment Reporting Information [Line Items]
Depreciation and amortization	131.3	135.6	147.2
Architecture & Software
Segment Reporting Information [Line Items]
Identifiable assets	1,793.6	1,410.5	1,788.9
Depreciation and amortization	61.5	63.8	72.5
Capital expenditures	33.3	57.7	29.4
Control Products & Solutions
Segment Reporting Information [Line Items]
Identifiable assets	2,791.0	2,114.8	2,094.9
Depreciation and amortization	68.0	69.6	72.4
Capital expenditures	$ 61.6	$ 68.9	$ 38.5