  Lur'e-type nonlinear systems are virtually ubiquitous in applied control
theory, which explains the great interest they have attracted throughout the
years. The purpose of this paper is to propose conditions to assess incremental
asymptotic stability of Lur'e systems that are less conservative than those
obtained with the incremental circle criterion. The method is based on the
approximation of the nonlinearity by a piecewise-affine function. The Lur'e
system can then be rewritten as a so-called piecewise-affine Lur'e system, for
which sufficient conditions for asymptotic incremental stability are provided.
These conditions are expressed as linear matrix inequalities (LMIs) allowing
the construction of a continuous piecewise-quadratic incremental Lyapunov
function, which can be efficiently solved numerically. The results are
illustrated with numerical examples.
