A relaxation method for stable inversion of discrete-time nonlinear systems [power converter application]

This paper formulates and solves the problem of stable inversion for a class of discrete-time nonlinear systems possessing hyperbolic zero dynamics. Given a desired output trajectory, the new stable inversion method determines bounded reference trajectories for the input and state variables that satisfy the plant state and output equations. For minimum-phase systems these reference trajectories are causal, whereas for nonminimum-phase systems they are noncausal. The numerical method proposed for stable inversion is based on iterative solution of simultaneous nonlinear equations using quasi-Newton schemes. An application to electronic power conversion circuits illustrates the significant benefits of computing the feedforward input using stable inversion.