MINIMIZATION OF THE MAXIMUM PEAK-TO-PEAK GAIN - THE GENERAL MULTIBLOCK PROBLEM

This paper presents a comprehensive study of the general l1-optimal multiblock problem, as well as a new linear programming algorithm 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 on the structure of the optimal solution, and different classes of multiblock problems are distinguished. This leads to conceptually attractive, iterative method for finding approximate solutions with the following properties: 1) approximates multiblock problems with one-block problems by delay augmentation, 2) unifies the treatment of zero and rank interpolation conditions through robust computations, 3) provides upper and lower bounds of the optimal objective function by solving one finite dimensional linear program at each iteration, 4) for a class of problems, it generates suboptimal controllers that achieve the upper bound without order inflation, 5) both bounds as well as the solution converge to the optimal, 6) it does not require the existence of polynomial feasible solutions, and 7) gives information about the support structure of the optimal solution.