Sliding surface design by quadratic stabilization and pole placement

The problem of the robust design of sliding surface for variable structure control systems is studied. The approach taken here is mainly based on pole placement in a sector of the left half-plane. The method uses the quadratic stabilizability concept and the LMI formalism to develop a usefull sufficient condition of robust pole placement in a sector. Associated to this condition, a convex optimization problem is developped. The design is systematic and rather simple.