Some properties of generalized inverse of non-square systems

Generalized inverse of non-square MIMO system arise from many application problems. This paper investigates some fundamental properties of the generalized inverse. These include the necessary and sufficient conditions for the minimum H₂ norm inverse, the minimality of the H₂ norms for the rows/columns of the inverse, and the redundancy and design freedom associated with the rows/columns of the generalized inverse. An application to MIMO communication system is presented to demonstrate the usefulness and potential of these properties.