LMI Formulation For The Resilient Dynamic Output Feedback Stabilization of Linear Periodic Systems

International audienceThis paper addresses the problem of full-order dynamic output-feedback stabilization for linear discrete time periodic systems. The adopted framework is based on the Lyapunov theory and uses the Linear Matrix Inequalities (LMI) formalism. The output-feedback design is tackled along with fragility issues. This is performed by the synthesis of convex sets of stabilizing controllers guaranteeing closed-loop resilience with respect to uncertainties on the controller parameters. Full-order dynamic output-feedback without resilience considerations is proved for the LTI case to have a convex LMI formulation. This result is extended here to the periodic case and the major contribution of the paper is to prove that the resilience can be as well handled with LMI formulations. This last result is new, even in the LTI framework