Generalized incremental homogeneity, incremental observability and global observer design

We introduce the notion of incremental generalized homogeneity, giving new results on observer design for systems with bounded trajectories and putting into a unifying framework constructive results for triangular (feedback/ feedforward) and homogeneous systems. An asymptotic state observer is designed by dominating the generalized homogeneity degree of the nonlinearities with the degree of the linear approximation of the observation error system. Incremental generalized homogeneity provides a high flexibility in the design of the observer gains and gives a systematic tool for the stabilization of systems with highly complex structures.