Diagonal dominance using LMIs

A new method for determining a constant precompensator for reducing the effects of interactions in multivariable systems is presented. It is shown that linear matrix inequalities (LMIs) can be used in the design of precompensators to achieve diagonal dominance. The algorithm presented alleviates the necessity of choosing a suitable frequency in designing such a precompensator, as required by previous methods. The method is then modified to reduce the conservatism by the introduction of scaling as an LMI variable and a path-shaping matrix. The path-shaping matrix enables a designer to find an optimal precompensator to achieve a specific forward path structure. The algorithm is applied to a Rolls Royce Spey jet engine, and the results obtained are comparable with previously obtained results. However, it gives a more systematic methodology for designing such precompensators.