Observer design for lipschitz nonlinear systems with state dependency and. nonlinearity distribution

Observer design method for Lipschitz nonlinear systems, reported in the literature, did not consider the distribution matrix of nonlinearity and state dependence of nonlinear functions in the state space model of nonlinear system. The proposed observer considers these matrices and a new sufficient condition for asymptotic stability is derived based on Linear Matrix Inequality (LMI) and demonstrated to be less conservative than the reported approach, in terms of maximum value of the Lipschitz constant of the nonlinearity for which asymptotic stability is guaranteed. The proposed method is applied on a practical example and it is shown that the Lipschitz constant value can be increased of the order of 105 times.