Robust Feedback Stabilization of Linear MIMO Systems Using Generalized Homogenization

A robust nonlinear control is designed for stabilizing linear multi-input-multi-output systems. The presented control law homogenizes a linear system (without its transformation to a canonical form) with a specified degree and stabilizes it in a finite time (or with a fixed-time attraction to any compact set containing the origin) if the degree of homogeneity is negative (positive). The tuning procedure is formalized in an linear matrix inequalities (LMI) form. Performance of the approach is illustrated by numerical and experimental examples.