Robust H∞ control of uncertain switched systems defined on polyhedral sets with Filippov solutions

► The robust stability and H∞ control problem of uncertain switched systems defined on polyhedral sets are investigated. ► The analysis is performed in the framework of Filippov solutions. ► The results are reformulated in terms of linear and bilinear matrix inequalities. ► The results are applicable to solutions with infinite switching in finite time and sliding modes. ► Two simulation examples corroborate the validity of the proposed methodologies.