Observer-based controller synthesis for LPV descriptor systems using dilated LMI conditions

This paper deals with the stabilization and the H₂ control synthesis of Linear Parameter Varying (LPV) descriptor systems. The compensator design problem is examined through a parameter-dependent observer-based control structure. The proposed approach uses parameter-dependent Lyapunov functions and involves slack variables in order to achieve less restrictive synthesis conditions. These synthesis conditions are expressed as a Linear Matrix Inequality (LMI) solvability problem. The admissibility and the H₂ performance are ensured by computing appropriate gains of the state-feedback controller and the observer. Simulation results obtained with a numerical example, show the effectiveness of the proposed approach.