A hybrid scheme for reducing peaking in high-gain observers for a class of nonlinear systems

For a family of nonlinearly interconnected second order plants, we propose a hybrid modification of the well known high-gain observer design, which leads to guaranteed asymptotic stability properties of the error dynamics, as well as exhibiting significantly reduced peaking. The hybrid modification results in suitable jumps of the observer state, which therefore corresponds to a discontinuous function of ordinary time. The jump conditions depend on the plant output and on extra states incorporated in the observer that evolve according to some suitable combination of the output error and of its integral. Our result is illustrated on a well known case study taken from the literature, and also on a planar robot with rigid links.