A Newton-Raphson algorithm for calculating the effects of changes in weights on an H_∞ design

When weights are adjusted in an H_∞ design, corresponding modifications occur in the synthesised H_∞ controller and the resulting closed-loop transfer function matrices of interest. This article proposes an algorithm that allow us to compute the corresponding modifications hi the controller and closed-loop transfer functions via calculations that are simpler/faster than solving two brand new Riccati equations from scratch. This is particularly beneficial (in terms of both speed and numerical reliability of the solutions) for high order systems and in iterative adaptive control algorithms that involve weight adjustments at each sampling interval. The algorithm proposed here builds upon our previous results presented in [1] and now allow us to also handle medium-size and large weight adjustments, as opposed to only small weight adjustments.