Robust GMVC algorithm undermining the employment of the Moore–Penrose inverse

In the paper, a set of new findings derived from the application of the nonunique $\sigma$-inverse into the generalized minimum variance control (GMVC) algorithm is given. In such a way, the robust instance of the discussed control strategy is proposed strictly devoted to the right-invertible LTI systems defined in the discrete-time transfer-function-originated framework. The alternative inverse-based control procedure clearly outperforms the classical one giving rise to the introduction of the generalized $\sigma$-inverse rather than the Moore-Penrose (MP) one. Two numerical examples address a huge impact of the so-called degrees of freedom at least in the minimum-energy considerations.