  Efficiently computable stability and performance analysis of nonlinear
systems becomes increasingly more important in practical applications.
Dissipativity can express stability and performance jointly, but existing
results are limited to the regions around the equilibrium points of these
nonlinear systems. The incremental framework, based on the convergence of the
system trajectories, removes this limitation. We investigate how stability and
performance characterizations of nonlinear systems in the incremental framework
are linked to dissipativity, and how general performance characterization
beyond the $\mathcal{L}_2$-gain concept can be understood in this framework.
This paper presents a matrix inequalities-based convex incremental
dissipativity analysis for nonlinear systems via quadratic storage and supply
functions. The proposed dissipativity analysis links the notions of
incremental, differential, and general dissipativity. We show that through
differential dissipativity, incremental and general dissipativity of the
nonlinear system can be guaranteed. These results also lead to the incremental
extensions of the $\mathcal{L}_2$-gain, the generalized $\mathcal{H}_2$-norm,
the $\mathcal{L}_\infty$-gain, and passivity of nonlinear systems.
