Parametric robust ℋ2 control design with generalized multipliers via LMI synthesis

This paper presents a new, combined analysis and synthesis procedure that provides an efficient and effective robust control design technique for systems with real parametric uncertainty. Robust stability is determined for these systems using passivity analysis with generalized multipliers, and the worst case ℋ₂ performance is investigated using a bound on the output energy. The dynamics of the multipliers are systematically chosen using knowledge from the uncertain system. The synthesis objective of minimizing the robust performance naturally leads to bilinear matrix inequalities, which can be decoupled to a large extent. A heuristic, iterative algorithm is presented to handle the residual coupling in the design problem. A simple beam example is used to demonstrate that the synthesis with generalized multipliers leads to less conservative controllers for systems with real parametric uncertainty