MIXED L(1) H-INFINITY CONTROL OF MIMO SYSTEMS VIA CONVEX-OPTIMIZATION/

Mixed performance control problems have been the object of much attent ion lately. These problems allow for capturing different performance s pecifications without resorting to approximations or the use of weight ing functions, thus eliminating the need for trial-and-error-type iter ations. In this paper we present a methodology for designing mixed l(1 )/H-infinity controllers for MIMO systems. These controllers allow for minimizing the worst case peak output due to persistent disturbances, while at the same time satisfying an H-infinity-norm constraint upon a given closed-loop transfer function. Therefore, they are of particul ar interest for applications dealing with multiple performance specifi cations 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) con trary to the H-2/H-infinity case, the l(1)/H-infinity problem admits a solution in l(1), and 2) rational suboptimal controllers can be obtai ned by solving a sequence of problems, each one consisting of a finite -dimensional convex optimization and a four-block H-infinity problem. Moreover, this sequence of controllers converges in the l(1) topology to an optimum.