L2 Observers for a Class of Nonlinear Systems with Unknown Inputs

We consider the problem of estimating the state and unknown input for a large class of nonlinear systems subject to unknown exogenous inputs. The exogenous inputs themselves are modeled as being generated by a nonlinear system subject to unknown inputs. The nonlinearities considered in this work are characterized by multiplier matrices that include many commonly encountered nonlinearities. We obtain a linear matrix inequality (LMI), that, if feasible, provides the gains for an observer which results in certified L-2 performance of the error dynamics associated with the observer. We also present conditions which guarantee that the L-2 norm of the error can be made arbitrarily small and investigate conditions for feasibility of the proposed LMIs.