Nonlinear Quasi-Unknown Input Observer Design Using Dissipativity

This paper addresses the design of nonlinear quasi-unknown input observers for systems that can be interpreted as an interconnection of a linear dynamical subsystem with a static nonlinear feedback subject to additive perturbations. As assumed classically an exosystem is considered describing the dynamics of the perturbation, meaning that the dynamical mechanisms giving rise to the perturbation are sufficiently well known but the underlying initial condition is unknown. Extending classical results based on the Sylvester equation, and combining them with well-established dissipativity concepts and design methods, a new approach for quasi-unknown input observer design is obtained. It simplifies previous work on general unknown input observer design by exploiting the structural knowledge about the exosystem, without extending the state dimension. The approach is illustrated with numerical case examples.