Robust Admissibilization of Descriptor LPV Systems based on SOF

The contribution of this work is focused on the analysis and synthesis of controllers based on static output feedback (SOF), for a class of descriptor linear parameter variable (LPV) systems. Descriptors systems, called also: differential-algebraic systems, singular systems, semi-state systems or generalized state-space systems; are considered to possess disturbances and parametric uncertainties of polytopic type, as are described by the following equation: Ez(t) = F(ρ)z(t) + B(ρ)ω(t) + Bu(t), h(t) = C(ρ)z(t), where ρ is a parametric variation. From a condition of existence of a linear injective application, representing the generalized inverse matrix of E, the original descriptor system is transformed to a LPV system. Then, the condition for the static output feedback on the LPV system is analyzed. Synthesis of the SOF-based controller is obtained considering performance indices in H₂ and H_∞, described as linear matrix inequalities, LMIs, as criteria in order to obtain the gain of SOF, in the presence of uncertainties and disturbances.