  This paper is concerned with incremental stability properties of nonlinear
systems. We propose conditions to compute an upper bound on the incremental
L2-gain and to assess incremental asymptotic stability of piecewise-affine
(PWA) systems. The conditions are derived from dissipativity analysis, and are
based on the construction of piecewise-quadratic functions via linear matrix
inequalities (LMI) that can be efficiently solved numerically. The developments
are shown to be less conservative than previous results, and are illustrated
with numerical examples. In the last part of this paper, we study the
connection between incremental L2-gain stability and incremental asymptotic
stability. It is shown that, with appropriate observability and reachability
assumptions on the input-output operator, incremental L2-gain implies
incremental asymptotic stability. Finally, it is shown that the converse
implication follows provided some regularity conditions on the state space
representation are met.
