New form of block matrix inversion

A block matrix inversion is a tool that is useful in areas of control, estimation theory and signal processing. However, one of two diagonal entries of the block matrices should be at least invertible to accomplish the conventional block matrix inversion. This paper shows that this assumption is partially released by offering new form of symbolic block matrix inversion. Though the suggested block matrix inversion can be applied to a variety of examples, in this paper, three application examples are suggested to show their effectiveness; the one is simply for finding an inverse matrix, another is for obtaining an inverse plant model of MIMO (multi-inputs and multi-outputs) plant for canceling plant noise and disturbance, and the other is for solving an optimization problem subject to an equality constraint, respectively.