Discrete-time lossless systems, feedback equivalence and passivity

In this paper we summarize and extend some recent results on the problem of when a discrete-time nonlinear system is feedback equivalent to a lossless system and the problem of global stabilization via smooth state feedback. In particular, we show how the criterion of zero-state detectability for discrete-time passive systems can be carried out in the absence of the KYP lemma, and how the feedback equivalence idea can be applied to stabilize a class of discrete-time nonlinear systems by means of smooth state feedback