Incremental generalized homogeneity, observer design and semiglobal stabilization

We introduce the notion of incremental generalized homogeneity, giving new results on semiglobal stabilization by output feedback and observer design and putting into a unifying framework the stabilization design for triangular (feedback/feedforward forms) and homogeneous systems. A state feedback controller and an asymptotic state observer are designed separately and an output feedback controller is obtained according to a certainty-equivalence principle. Non-homogeneity introduces a high flexibility in the choice of the controller/observer gains and gives a systematic tool for the stabilization of systems with highly complex structures.