Resilient design of discrete-time 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 plant equations. This paper addresses the important problem of resilience or non-fragility which is the maintenance of convergence or performance when the observer is erroneously implemented due possibly to computational errors, i.e. round off errors in digital implementation or actuator errors, etc. A linear matrix inequality approach is presented that maximizes performance in the implementation based on the knowledge of an upper bound on the error in the observer gain. Simulation examples complement the theoretical results.