Conditions for C-controllability and C-observability of Rectangular Descriptor Systems

The generalized inverse form of a rectangular descriptor system is proposed. Unlike the relationship between the inverse form and a regular descriptor system, controllability and observability of the generalized inverse form are not equivalent to C-controllability and C-observability of the original system. It can be also found that conditions for C-controllability and C-observability of a rectangular descriptor system are not dual under the generalized inverse form