Additive state decomposition

   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 = np + ns and P = Pp ⊕ Ps. By contrast, the additive state decomposition satisfies n = np = ns and P = Pp + Ps.