Convex Conditions for Observer Design in Nonlinear Continuous-Time Systems Using a Spatial Discretization Procedure

This paper proposes convex conditions for the observer design of nonlinear continuous-time systems. A broad class of nonlinear systems can be tackled by the proposed technique. A spatial discretization is employed, and an approximate model is obtained within the error matrices that measure the difference between the nonlinear system and the approximated one. The conditions are formulated as parameter-dependent matrix inequalities and ensure that the observer can asymptotically follow the states of the original nonlinear system while guaranteeing a bound to the L 2 -gain from the disturbance input to the estimation error. Numerical experiments are used to illustrate the features of the proposed method.