Inverse-based methods to minimum-energy MV control for nonsquare state-space systems

The paper presents an approach to the synthesis of MV control systems with respect to minimum-energy of the control inputs. Due to the reason, a recently introduced polynomial matrix σ-inverse is applied to LTI nonsquare systems described by discrete-time state-space framework. It is shown that classical minimum-norm right inverse is not sufficient to obtain the minimum-energy of control runs. Thus, the σ-inverse with parameter/polynomial, so-called degrees of freedom, gives better results than typical Moore-Penrose inverse in terms of said lower energy. The effectiveness of the presented method is confirmed by simulation examples in Matlab environment.