Resilient design of Thau´s observer using LMIs

Much of the recent work on robust observer design has focused on the convergence of the observer in the presence of parameter perturbations in the plant equations. The present work addresses the important problem of resilience or non-fragility, which is maintenance of convergence when the observer is erroneously implemented due possibly to computational errors. A class of nonlinear system and measurement equations is considered and a linear matrix inequality approach is presented that guarantees convergence based on the knowledge of an upper bound on the observer gain perturbations. This result can be viewed as the resilient version of Thau´s method of nonlinear observer design.