High gain observer for a class of implicit systems

Under some observability assumptions (uniform observability), a high gain observer for a class of implicit dynamical systems is given. Numerically, the computation of trajectories of such implicit systems usually necessitates the use of an optimization algorithm together with an ODE numerical method. This complicates the synthesis of an observer. The observer design proposed here leads to a classical dynamical system defined on some R^N, with N⩾n, n being the dimension of the state space of the implicit system