Extensions on a certainty-equivalence feedback design with a class of feedbacks which guarantee ISS

In this paper a new class of nonlinear feedbacks that guarantee input-to-state stability (ISS) w.r.t. the measurement error is identified. In particular, it is shown that (inverse) optimal feedback laws, that are separable into a globally Lipschitz part and a nonlinearity satisfying a certain inequality condition, guarantee ISS. As a consequence, those state feedbacks in conjunction with any globally asymptotically convergent observer lead to a globally asymptotically stable closed-loop. The theoretical results are applied to several control problems, e.g. the nonlinear output feedback design of a single-link robot arm or an active magnetic bearing system.