Weight optimisation in H∞ loop-shaping

An optimisation problem is introduced which integrates a number of steps of the standard H∞ loop-shaping design procedure. This optimisation problem maximises the robust stability margin over allowable loop-shaping weights while ensuring that the resulting loop-shape lives in a pre-defined region that characterises the desired performance specifications. The resulting algorithm thus considerably facilitates the design of loop-shaping weights by giving the designer an indication of what is attainable and hence allows the designer to concentrate on more fundamental design issues than simply finding weights that achieve a desired loop-shape.