H/sub 2//H/sub /spl infin// filter design for systems with polytope-bounded uncertainty

This correspondence presents a strategy for robust H/sub 2//H/sub /spl infin// filtering design, with regional pole placement, applied to discrete- or continuous-time linear time-invariant (LTI) systems with polytope-bounded uncertainty. To overcome the conservatism of linear matrix inequality (LMI)-based formulations, the proposed design approach is based on a multiobjective optimization algorithm applied directly in the space of the filter parameters. The H/sub 2/ and H/sub /spl infin// norms, computed in all polytope vertices and in possible "worst case" interior points, are taken as the optimization objectives. A combination of branch-and-bound algorithm and LMI guaranteed cost formulations is applied to compute the coordinates of the worst case norms and to validate the filter design to the whole polytope. Examples are presented to illustrate the effectiveness of the proposed strategy.