Revenue Recognition - Disaggregation of Revenue by Operating Segment and by Geographic Region (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Mar. 31, 2024	Mar. 31, 2023	Mar. 31, 2024	Mar. 31, 2023
Disaggregation of Revenue [Line Items]
Sales	$ 2,126.0	$ 2,275.4	$ 4,178.1	$ 4,256.4
North America
Disaggregation of Revenue [Line Items]
Sales	1,293.6	1,310.6	2,540.7	2,489.5
Europe, Middle East, and Africa
Disaggregation of Revenue [Line Items]
Sales	398.9	486.5	787.2	859.3
Asia Pacific
Disaggregation of Revenue [Line Items]
Sales	269.9	334.2	545.5	630.7
Latin America
Disaggregation of Revenue [Line Items]
Sales	163.6	144.1	304.7	276.9
Intelligent Devices
Disaggregation of Revenue [Line Items]
Sales	973.5	1,023.2	1,900.8	1,959.4
Intelligent Devices | North America
Disaggregation of Revenue [Line Items]
Sales	636.6	598.7	1,240.9	1,166.1
Intelligent Devices | Europe, Middle East, and Africa
Disaggregation of Revenue [Line Items]
Sales	158.1	216.6	324.7	387.8
Intelligent Devices | Asia Pacific
Disaggregation of Revenue [Line Items]
Sales	100.3	136.7	198.2	268.0
Intelligent Devices | Latin America
Disaggregation of Revenue [Line Items]
Sales	78.5	71.2	137.0	137.5
Software & Control
Disaggregation of Revenue [Line Items]
Sales	570.0	741.1	1,173.6	1,314.4
Software & Control | North America
Disaggregation of Revenue [Line Items]
Sales	362.7	452.0	749.3	836.1
Software & Control | Europe, Middle East, and Africa
Disaggregation of Revenue [Line Items]
Sales	96.1	148.6	195.9	234.4
Software & Control | Asia Pacific
Disaggregation of Revenue [Line Items]
Sales	69.8	99.6	148.8	168.0
Software & Control | Latin America
Disaggregation of Revenue [Line Items]
Sales	41.4	40.9	79.6	75.9
Lifecycle Services
Disaggregation of Revenue [Line Items]
Sales	582.5	511.1	1,103.7	982.6
Lifecycle Services | North America
Disaggregation of Revenue [Line Items]
Sales	294.3	259.9	550.5	487.3
Lifecycle Services | Europe, Middle East, and Africa
Disaggregation of Revenue [Line Items]
Sales	144.7	121.3	266.6	237.1
Lifecycle Services | Asia Pacific
Disaggregation of Revenue [Line Items]
Sales	99.8	97.9	198.5	194.7
Lifecycle Services | Latin America
Disaggregation of Revenue [Line Items]
Sales	$ 43.7	$ 32.0	$ 88.1	$ 63.5