Control design with transfer functions associated to higher order Volterra kernels

The Volterra series provides a convolution-oriented method for representing the input/output behavior of a nonlinear system. For the case of constant system parameters, such a representation is naturally suited to control design with transfer functions: zeroth order, first order, second order, and so forth. In 1979, Peczkowski, Sain, and Leake[1] introduced a Total Synthesis Problem (TSP) approach to linear feed-back synthesis; and in 1981, Peczkowski and Sain[2] demonstrated how to schedule TSP into a nonlinear controller. For plants with one input and one output, Al-Baiyat and Sain [3] extended TSP to higher order transfer functions for the class of linear analytic systems. In this paper, we complete the extension by treating multiple inputs and multiple outputs. The method is illustrated by designing a control system for a DC to AC converter.