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