Resilient Static Output Feedback Stabilization of Linear Periodic Systems
Résumé
This paper adresses the problem of static 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. Two design problems are solved: static periodic and static non-periodic output-feedback. Proposed solutions are based on non-convex optimization but may be solved with appropriate non-optimal algorithms and this is illustrated on various examples.