New Expressions of 2 $\,\times\,$2 Block Matrix Inversion and Their Application

A 2$\,\times\,$ 2 block matrix inversion is a tool that is frequently used in areas of control, estimation theory and signal processing. However, one of the two diagonal entries of the block matrix should be invertible to carry out a conventional block matrix inversion. In this technical note, we show that this assumption can be partially released with three new types of symbolic block matrix inversion. Also, an application example of an inverse plant model of a multi-inputs and multi-output (MIMO) plant, which cancels plant noise and disturbance, is suggested to show the effectiveness of these new types of matrix inversion.