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Efficiently computable stability and performance analysis of nonlinear systems becomes increasingly more important in practical applications. An important notion connecting stability and performance is dissipativity. However, this property is usually only valid around an equilibrium point of the nonlinear system and usually involves cumbersome computations to find a valid storage function. Analyzing stability using the trajectories of the nonlinear system, i.e. incremental stability analysis, has shown to solve the first issue. However, how stability and performance characterizations of nonlinear systems in the incremental framework are linked to dissipativity, and how general performance characterization beyond the L2-gain concept can be understood in the incremental framework is largely unknown. By systematically establishing the missing links, this paper presents a matrix inequality based convex dissipativity analysis with the use of quadratic storage and supply functions, for a rather general class of systems with smooth nonlinearities. The proposed dissipativity analysis links the notions of differential, incremental and general dissipativity by a chain of implications. We show that through differential dissipativity, we give guarantees on incremental and general dissipativity of the nonlinear system. Using the results from the aforementioned chain of implications, incremental extensions for the analysis of L2-gain, the generalized H2-norm, L∞-gain and passivity of a nonlinear system are presented. Moreover, we give a convex computation method to solve the obtained conditions. The effectiveness of the analysis tools are demonstrated by means of an academic example.

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