Mixed Control of MIMO Systems via Convex Optimization

Mixed performance control problems have been the object of much attention lately. These problems allow for capturing different performance specifications without resorting to approximations or the use of weighting functions, thus eliminating the need for trial-and-error-type iterations. In this paper we present a methodology for designing mixed l1=H1 controllers for MIMO systems. These controllers allow for minimizing the worst case peak output due to persistent disturbances, while at the same time satisfying anH1-norm constraint upon a given closedloop transfer function. Therefore, they are of particular interest for applications dealing with multiple performance specifications given in terms of the worst case peak values, both in the time and frequency domains. The main results of the paper show that 1) contrary to the H2=H1 case, the l1=H1 problem admits a solution in l1, and 2) rational suboptimal controllers can be obtained by solving a sequence of problems, each one consisting of a finite-dimensional convex optimization and a four-block H1 problem. Moreover, this sequence of controllers converges in the l1 topology to an optimum.