On multiobjective synthesis for parameter-dependent descriptor systems

This note proposes dilated (or extended) linear matrix inequality (LMI) characterisations of admissibility, D-admissibility, H _?? and H ₂ norms for continuous-time descriptor systems. As for state-space systems, these LMIs achieve less conservative results when dealing with robust admissibility/performance analysis of affine parameter-dependent descriptor systems. Furthermore, an iterative design procedure for multiobjective state-feedback control of parameter-dependent descriptor systems is presented based on these dilated LMI conditions. The main idea underlying the proposed method is to linearise the products of controller parameter and the auxiliary variable by assigning the last one. In the initialisation step of the proposed algorithm, the assignment takes into account an explicit characterisation of the auxiliary variable. The effectiveness of the proposed conditions and design method is shown through some numerical examples.