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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.