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MIMOl 1-optimization with a scalar control

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Abstract

In Ref. 1, the author showed that some scalar mixed sensitivity minimization problems have rationall 1-optimal solutions and computed these solutions. Here, a similar approach is applied to a multi-input multi-output (MIMO) plant. The general flavor of the solution is the same as in Ref. 1, but there is one distinct new feature. We prove that some of the outputs may be ignored, in the sense that they have no influence on the optimal solution and that all the operators corresponding to the remaining outputs have the same optimal norm. This fact suggests alternative methods for solving the problem and it is employed in the construction of an exact rationall 1-optimal solution of a particular problem.

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Authors and Affiliations

  1. Institute of Mathematics, Helsinki University of Technology, Espoo, Finland

    O. J. Staffans (Docent)

Authors
  1. O. J. Staffans
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Additional information

Communicated by J. B. Pearson

This work was partly done while the author was a visiting professor at the Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia. Supported in part by a joint grant from NSF and the Academy of Finland.

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Staffans, O.J. MIMOl 1-optimization with a scalar control. J Optim Theory Appl 74, 545–564 (1992). https://doi.org/10.1007/BF00940326

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