Resilient design of observers with general criteria using LMIs

Much of the recent work on robust control or observer design has focused on preservation of stability of the controlled system or the convergence of the observer in the presence of parameter perturbations in the system and/or measurement equations. The present work addresses the important problem of resilience or non-fragility of observers, which is the maintenance of convergence or performance when the observer gain is perturbed due possibly to computational or implementation errors. A linear matrix inequality approach is presented that maximizes performance of the observer based on the knowledge of an upper bound on the error in the observer gain. Simulation studies are included to test the conservativeness of this design procedure