On the computation of the general l1 multiblock problem

The authors present a comprehensive study of the general l₁ optimal multiblock problem, as well as a new method for computing suboptimal controllers. By formulating the interpolation conditions in a concise and natural way, the general theory is developed in simpler terms and with a minimum number of assumptions. In addition, further insight is gained into the structure of the optimal solution, and different classes of multiblock problems are distinguished. This leads to a conceptually attractive, iterative method for finding approximate solutions that approximates multiblock problems with one-block problems by delay augmentation, unifies the treatment of zero and rank interpolation conditions, provides upper and lower bounds of the optimal objective function by solving one finite dimensional linear program at each iteration, and, for a class of problems, generates suboptimal controllers that achieve the upper bound without order inflation. With this method, both bounds and the solution converge to the optimal, and it does not require the existence of polynomial feasible solutions