Inversion of nonlinear and time-varying systems

This paper is concerned with the inversion of implementations for systems that may generally be nonlinear and time-varying. Specifically, techniques are presented for modifying an implementation of a forward system, represented as an interconnection of subsystems, in such a way that an implementation for the inverse system is obtained. We focus on a class of modifications that leave subsystems in the inverse system unchanged with respect to those in the forward implementation. The techniques are therefore well-suited to the design of matched pre-emphasis and de-emphasis filters, as approximations due to coefficient quantization in the forward system are naturally matched in the inverse. In performing the inversion, an explicit input-output characterization of the system is not required, although the forward system must be known to be invertible. The techniques are applied to the inversion of nonlinear and time-varying systems, as well as to the problem of sparse matrix inversion.