Analysis and Synthesis of Nonlinear Systems

The input-output relation of linear systems (convolution integral) is generalized to a class of nonlinear systems. This class is represented by analytic functionals as studied by Volterra and Fréchet. The analysis can be performed by measuring the response of nonlinear systems to series of impulse functions. The synthesis involves linear systems, zero-memory nonlinear systems and multiple multipliers in the general case, noninteracting linear and zero-memory nonlinear systems in many practical cases. Physically, the class of analytical functionals describes systems obtained by cascading noninteracting linear and zero-memory non-linear systems in open or closed loop configuration. Orthogonal representations of nonlinear systems are considered; for bounded signals and in particular for sinusoidal signals, the Tchebycheff polynomials representation is shown to be especially convenient.