  This paper considers the equilibrium-free stability and performance analysis
of discrete-time nonlinear systems. We consider two types of equilibrium-free
notions. Namely, the universal shifted concept, which considers stability and
performance w.r.t. all equilibrium points of the system, and the incremental
concept, which considers stability and performance between trajectories of the
system. In this paper, we show how universal shifted stability and performance
of discrete-time systems can be analyzed by making use of the time-difference
dynamics. Moreover, we extend the existing results for incremental
dissipativity for discrete-time systems based on dissipativity analysis of the
differential dynamics to more general state-dependent storage functions for
less conservative results. Finally, we show how both these equilibrium-free
notions can be cast as a convex analysis problem by making use of the linear
parameter-varying framework, which is also demonstrated by means of an example.
