A New Generalized Θ-Inverse vs. Moore-Penrose Structure: A Comparative Control-Oriented Practical Investigation

Abstract

A new non-unique $\Theta $ -inverse of non-square polynomial matrices is presented in this paper. It is shown that the above inverse specializes to the unique Moore-Penrose one under several specific assumptions. Due to the existence of some degrees of freedom, the $\Theta $ -inverse outperforms the Moore-Penrose inverse in various inverse-related problems covering the multivariable control theory. In many scenarios the former inverse can stabilize a closed-loop control plant being unstable by application of the Moore-Penrose formula. Practical and theoretical simulation examples confirm the correctness of the proposed method.

Keywords

• Generalized inverses
• polynomial matrices
• non-square matrices
• Moore-Penrose inverse
• optimal control
• perfect control