Calculation of non-mixed second derivatives in multirate systems through signal flow graph techniques

This paper proposes a new approach for calculation of derivatives in general multirate systems through a signal flow graph (SFG) technique. The first original aspect consists of the derivation of an adjoint graph without using Lee´s theorem. Secondly, such a graph is able to deliver not only the first derivatives but also the full second derivatives of an output of the initial system with respect to the node variables of the starting SFG. Some examples are reported to show the right way of working of the proposed method on derivative calculation in general situations. Hence, the overall algorithm represents a useful tool for determination of Jacobean and Hessian based information in learning systems, as was already done in other related but less general contributions in the literature.