On increasing-gain observers for nonlinear continuous-time systems

We deal with the problem of constructing state observers for nonlinear continuous-time systems. We focus on increasing-gain observers, which have been recently proposed as generalization of high-gain observers because of a time-varying gain that is let to be small in the first time instants, increases over time up to a maximum. As a novelty with respect to the literature on high-gain observer, the proof of stability is obtained by using a Lyapunov functional, thus allowing to accomplish the observer design with a reduced peaking. As a new contribution, we relax the system assumptions under which the global asymptotic stability of the estimation error is proved. The stability of the estimation error for the proposed observer is ensured by assuming a Lipschitz upper bound to which an exponentially decreasing term is added.