Nonlinear circle-criterion observers in discrete-time

Circle-criterion approach to discrete-time nonlinear observer design is presented. The new design method is mainly devoted to either bounded-state nonlinear systems or globally Lipschitz ones. The conditions of existence of globally converging observers are given in terms of a set of numerically tractable linear matrix inequalities. It is shown that the proposed algorithm is able to deal with both nonlinear systems with extremely high Lipschitz constants and nonlinear systems subject to either positive and non-positive slope nonlinearities. The efficacy of the proposed design procedure is testified through numerical examples.