Design of time-varying state observers for nonlinear systems by using input-to-state stability

The problem of constructing full-order state observers for nonlinear systems is addressed by resorting to input-to-state stability (ISS) as a tool of analysis. Instead of using standard Lyapunov functions, we explicitly search for ISS Lyapunov functions of the estimation error with respect to the external disturbances that act on the system and measurement equations. First, the use of ISS is motivated when dealing with the design of observers for quite a general class of nonlinear systems. Second, high-gain observers are investigated by providing conditions that ensure ISS as well as a given attenuation with respect to the noises in terms of L₂-gain. Third, an adaptive high-gain observer is proposed with such stability properties, which can be taken into account for the purpose of design by using linear matrix inequalities.