Incremental generalized homogeneity, observer design and semiglobal stabilization

The notion of incremental generalized homogeneity is introduced, 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) and homogeneous systems. A state feedback controller and an asymptotic state observer are designed separately by dominating the generalized homogeneity degree of the nonlinearities with the degree of the linear approximation of the system and an output feedback controller is obtained according to a certainty-equivalence principle

Lyapunov-based design of iISS feedforward systems with uncertainty and noisy measurements

We study the problem of achieving integral input to state stability (iISS) with respect to noise for a class of upper triangular nonlinear systems with uncertainty and measurement noise. We propose a novel step‐by‐step Lyapunov‐based design, consisting of (1) splitting an n‐dimensional system into n one‐dimensional systems, each with its own state, inputs, and measurement, (2) constructing a one‐dimensional measurement feedback controller for each one‐dimensional system, according to a certainty equivalence principle, and (3) selecting the parameters of these controllers so that their interconnection gives a measurement feedback controller for the n‐dimensional system. The stability analysis is performed through filtered Lyapunov functions, which are Lyapunov functions with parameters being the output of suitable dynamical filters