An application of polynomial matrix σ-inverse in minimum-energy state-space perfect control of nonsquare LTI MIMO systems

In this paper a concept of application of polynomial matrix σ-inverse in multivariable state-space perfect control is presented. The new inverse is derived from perfect control of systems described by the input-output approach. Rather surprisingly, the σ-inverse clearly outperforms some other inverses of nonsquare parameter matrices, including the classical minimum-norm right one. A minimum-energy simulation example made in Matlab/Simulink confirms the usefulness of the proposed method.