Mixed l/sub 1//H/sub /spl infin// control of MIMO systems via convex optimization

We present a methodology for designing mixed l/sub 1//H/sub /spl infin// 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/sub /spl infin//-norm constraint upon a given closed loop 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 H/sub 2//H/sub /spl infin// case, the l/sub 1//H/sub /spl infin// problem admits a solution in l/sub 1/; 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 H/sub /spl infin// problem. Moreover, this sequence of controllers converges in the l/sub 1/ topology to an optimum.