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Acquisitions - Narrative (Details) - USD ($)
$ in Millions
1 Months Ended 12 Months Ended
Aug. 31, 2021
Aug. 31, 2021
Sep. 30, 2023
Sep. 30, 2022
Sep. 30, 2021
Dec. 31, 2021
Business Acquisition [Line Items]            
Pro forma revenue     $ 88.3      
Goodwill     3,529.2 $ 3,524.0 $ 3,625.9  
Software & Control            
Business Acquisition [Line Items]            
Goodwill     2,420.1 2,398.7 2,447.5  
Fiscal 2023 Acquisitions            
Business Acquisition [Line Items]            
Pro forma revenue     9,100.0 7,900.0    
Business Acquisition, Pro Forma Net Income (Loss)     0.0 0.0    
Fiscal 2022 Acquisitions            
Business Acquisition [Line Items]            
Pro forma revenue     7,800.0 7,000.0    
Fiscal 2021 Acquisitions            
Business Acquisition [Line Items]            
Pro forma revenue       7,200.0 $ 6,500.0  
Sales       $ 27.9    
Plex Systems            
Business Acquisition [Line Items]            
Acquired finite-lived intangible assets, weighted average useful life   12 years        
Customer attrition rate 5.00%          
Royalty rate 25.00%          
Obsolescence factor phase out period 10 years          
Goodwill $ 1,730.0 $ 1,730.0        
Plex Systems | Customer relationships            
Business Acquisition [Line Items]            
Finite-lived intangible assets acquired 276.4          
Plex Systems | Patented Technology            
Business Acquisition [Line Items]            
Finite-lived intangible assets acquired 232.8          
Plex Systems | Trade Names            
Business Acquisition [Line Items]            
Finite-lived intangible assets acquired $ 22.2          
Oylo And Fiix Inc.            
Business Acquisition [Line Items]            
Goodwill           $ 224.8
Oylo And Fiix Inc. | Customer Relationships, Technology, and Trade Names            
Business Acquisition [Line Items]            
Finite-lived intangible assets acquired     $ 69.6      
Acquired finite-lived intangible assets, weighted average useful life     11 years      
Oylo And Fiix Inc. | Lifecycle Services            
Business Acquisition [Line Items]            
Goodwill     $ 12.8      
Oylo And Fiix Inc. | Software & Control            
Business Acquisition [Line Items]            
Goodwill     $ 212.0