Linear modeling error and steady-state behaviour of nonlinear dynamical systems

We consider different measures of nonlinearity that quantify the modeling error of optimal linear models for nonlinear systems. We show that linear dynamic approximations have no advantage over linear static approximations for static nonlinear functions in any of the considered measures. Simplified formulae for scalar nonlinearities are derived using the notion of a sector nonlinearity. We show that the steady state behaviour of a nonlinear system gives rise to a lower bound on the nonlinearity measures. Furthermore, some results for composite nonlinear systems are given.