Hybrid high-gain observers without peaking for planar nonlinear systems

In this paper we use hybrid techniques to augment high-gain observers for second order nonlinear plant with suitable reset rules where the state of the observer experiences an instantaneous jump if suitable conditions hold. These jump conditions depend on the plant output and on extra states incorporated in the observer which evolve according to some suitable combination of the output error and of its integral. We show that these hybrid rules succeed at removing peaking and illustrate our result on well known case studies taken from the literature.