Additive state decomposition

Additive state decomposition occurs when a <a href="/facts/System/hmqQ4ASX">system</a> is decomposed into two or more <a href="/facts/Subsystem/hmqQ4ASX">subsystems</a> with the same <a href="/facts/Dimension/0ktmUyac">dimension</a> as that of the original system. A commonly used decomposition in the control field is to decompose a system into two or more lower-order subsystems, called lower-order subsystem decomposition here. In contrast, additive state decomposition is to decompose a system into two or more subsystems with the same dimension as that of the original system.
Taking a system P for example, it is decomposed into two subsystems: Pp and Ps, where dim(Pp) = np and dim(Ps) = ns, respectively. The lower-order subsystem decomposition satisfies

n
        =
        
          n
          
            p
          
        
        +
        
          n
          
            s
          
        
        
           and 
        
        P
        =
        
          P
          
            p
          
        
        ⊕
        
          P
          
            s
          
        
      
    
    {\displaystyle n=n_{p}+n_{s}{\text{ and }}P=P_{p}\oplus P_{s}}

By contrast, the additive state decomposition satisfies

n
        =
        
          n
          
            p
          
        
        =
        
          n
          
            s
          
        
        
           and 
        
        P
        =
        
          P
          
            p
          
        
        +
        
          P
          
            s
          
        
      
    
    {\displaystyle n=n_{p}=n_{s}{\text{ and }}P=P_{p}+P_{s}}

Additive state decomposition open-in-new

Additive state decomposition