A Linear Algebraic Framework for the Analysis of Discrete-Time Nonlinear Systems

A linear algebraic framework for the analysis of synthesis-type problems for discrete-time nonlinear systems is introduced. This is an extension of a similar tool for continuous-time systems that established important connections between many algorithms associated with right-invertibility, left-invertibility and dynamic decoupling, as well as between these algorithms and an approach based upon differential algebra. A similar payoff is seen to be possible in the discrete-time setting.