On the influence of weight modification in H∞ control design

H_∞ control design is generally performed iteratively. At each iteration, the weights constraining the desired closed loop transfer functions are adapted. The way in which the weights are adapted is generally purely heuristic. It is consequently very interesting to build some insights about the influence of a weight modification on the obtained (central) controller and, more importantly, on the obtained closed-loop transfer functions. In this paper, we analyze this influence in the case of a classical two-block problem under the assumption of "small" modifications in the weights. The concept small modification must be understood in the sense of small enough to allow first order approximation.