Nonlinearity measures for data-driven system analysis and control

The paper deals with nonlinearity measures that quantify the nonlinearity of dynamical systems by the deviation to their `best' linear approximation. We link these measures to conic relations and dynamic conic sectors. Moreover, a characterization of stability for feedback interconnections using nonlinearity measures is derived. Furthermore, we calculate guaranteed lower and upper bounds for nonlinearity measures from a finite number of input-output samples.