Improved optimisation approach to the robust H2/H∞ control problem for linear systems

A strategy for robust H₂/H_∞ state-feedback control synthesis, with regional pole placement, applied to continuous- or discrete-time linear time-invariant uncertain systems is presented. It is based on a multiobjective optimisation over the space of the controller parameters. In the case of systems with polytope-bounded uncertainty, the H₂ and H_∞ norms, calculated in all polytope vertices and in possible ´worst case´ interior points are taken as the optimisation objectives. An a posteriori exact cost norm computation based on a branch-and-bound algorithm is applied for closed-loop performance assessment. The proposed strategy is applied to continuous- and discrete-time examples, including the design of a decentralised controller, and the results are compared with LMI-based formulations.