A new parametrization for static output feedback control of LPV discrete-time systems (Q2021315)

The papers considers output feedback control of linear discrete time parameter varying control systems. Here, the parameters are assumed to belong to the unit simplex and the particular goal is to design a static feedback law which is stabilizing for all possible parameters values. Additionally, an a priori specified \(\ell_2\) gain should be ensured. The main result of the paper (Theorem 1) provides sufficient conditions for the existence of a static output satisfying these conditions in form of a parameter-dependent family of linear matrix inequalities. Due to the numerical infeasibility, the authors relax the assumptions on the parameters and, for the numerical examples, consider affined parameter dependencies. Several numerical examples validate the theoretical findings.