Incremental ℒ2-gain analysis of piecewise-affine systems using piecewise quadratic storage functions

In this paper we are interested in the incremental stability of piecewise-affine (PWA) systems. We present conditions to compute an upper bound on the incremental ℒ2-gain based on dissipativity analysis. These conditions are expressed as linear matrix inequalities (LMI) allowing the construction of a continuous piecewise quadratic storage function. It is also shown that these conditions imply incremental asymptotic stability of the system. The result is illustrated with numerical examples.