On the strong stabilizability of MIMO n-dimensional linear systems

A plant is strongly stabilizable if there exists a stable compensator to stabilize it. This paper presents necessary conditions for the strong stabilizability of complex and real n-dimensional MIMO shift-invariant linear plants. For the real case, the condition is a generalization of the parity interlacing property of Youla et al. for the strong stabilizability of a real 1D MIMO plant. These conditions are also sufficient for the cases of n-D plants with a single output (MISO) or with a single input (SIMO). For general n-D MIMO plants, we do not know if the conditions are sufficient or not. A useful sufficient, but not necessary, condition for the strong stabilizability of a class of n-D (n⩾2) MIMO plants is given