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Mixed l1/H control of MIMO systems via convex optimization

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2 Author(s)
Sznaier, M. ; Dept. of Electr. Eng., Pennsylvania State Univ., University Park, PA, USA ; Bu, J.

We present a methodology for designing mixed l1/H 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-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 H2/H case, the l1/H 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 H problem. Moreover, this sequence of controllers converges in the l1 topology to an optimum

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Automatic Control, IEEE Transactions on  (Volume:43 ,  Issue: 9 )