L2 Observers for a Class of Nonlinear Systems with Unknown Inputs

Abstract: 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 L2 performance of the error dynamics associated with the observer. We also present conditions which guarantee that the L2 norm of the error can be made arbitrarily small and investigate conditions for feasibility of the proposed LMIs.