General stable factor perturbation controllers

The question of robustness results, in many cases, in an H_∞ problem. This paper solves the robustness problem for systems described by stable factor perturbations. First a general case is solved and then the special case when the nominal plant has normalized factors (NF). The solution of the general case needs only one solution to an indefinite Riccati equation, which is a considerable reduction in computational burden, compared to the general H_∞ problem. But this solution is dependent on ε and thus iterations are required. In the case of the normalized factor perturbation, the indefinite Riccati equation decouples into two definite Riccati equations, both of which are independent of ε. The normalized factor case was solved by Glover-McFarlane (1989, 1990) using Nehari extension theory. There are several reasons for solving the stable factor robustness problem for cases other than the normalized one. First, the robustness bound, ε, is highly dependent on which stable factor (found by using spectral factorization) is used. And second, some specific problems may not be well suited for normalized factors