H∞ control synthesis via reduced-order LMIs

Linear matrix inequality-based approaches for H-infinity control synthesis for systems with weighting functions possibly face numerical ill-conditioning and heavy computation. In this paper, by exploiting the potential pole/zero cancellation (mostly modes of weighting functions) in the closed-loop system, a new formulation is presented to find a full-order controller via reduced-order LMIs (linear matrix inequalities) and fewer decision variables. As a result, both numerical conditioning and numerical efficiency are improved. In addition, the new formulation is directly applicable to servomechanism problems where unstable disturbance dynamics are appended for robust regulation.