Stability of Lur´e systems with piecewise linear sector bounds

We consider the stability problem of Lur´e systems composed by a dynamical linear time invariant system closed in feedback through a static mapping belonging to a region bounded by piecewise linear characteristics. By exploiting the complementarity framework a model of the region expressed through constrained relations is obtained. Classical conic sectors representations can be derived as a particular case of the proposed model. The region representation is exploited to prove absolute stability of the Lur´e system in terms of cone-constrained linear matrix inequalities.