Differential stability and robust control of nonlinear systems
This paper deals with the problem of the robust input-output stabilization of nonlinear systems. The key machinery is provided by an extension of the gap metric, referred to as the differentiable gap between nonlinear dynamical systems which possess a differentiable graph, i.e. that admit an approximation by a linear system about any input- output bounded trajectory. The differentiable gap is a pseudo-metric in the sense that two different dynamical systems may have zero differentiable gap. However, it is still well suited for a quantitative description of the robustness of stability in a feedback interconnection. In fact, system perturbations are measured with the differentiable gap. The robustness of stability of a stable feedback interconnection is characterized in terms of a minimal opening between two nonlinear manifolds (system and controller graphs).
robust input-output stabilization of nonlinear systems
scientific article; zbMATH DE number 618215
scientific article