Exponential State Observers for Nonlinear Systems with Incremental Quadratic Constraints and Output Nonlinearities

This paper considers the exponential observer design for a class of nonlinear systems with output nonlinearities. The nonlinear terms in the systems are assumed to satisfy incremental quadratic constraints which include many commonly encountered nonlinearities in existing literature as some special cases. We construct a circle-criterion-based observer by injecting both the linear and the nonlinear output error terms into the observer system. Sufficient conditions ensuring the exponential stability of the proposed observer are established and formulated in terms of linear matrix inequalities. Finally, the advantages and effectiveness of the proposed design approach are illustrated through two examples.