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Transfer Function Optimization Procedure for the H 2/H ∞ Problem

Author

Listed:
  • G.O. Corrêa

    (National Laboratory for Scientific Computing, Petrópolis)

  • D. M. Sales

    (Army Polytechnic School)

Abstract

In this paper, the H 2/H ∞ problem is considered in a transfer-function setting, i.e., without a priori chosen bounds on the controller order. An optimization procedure is described which is based on a parametrization of all feasible descending directions stemming from a given point of the feasible transfer-function set. A search direction at each such point can be obtained on the basis of the solution of a convex finite-dimensional problem which can be converted into a LMI problem. Moving along the chosen direction in each step, the procedure in question generates a sequence of feasible points whose cost functional values converge to the optimal value of the H 2/H ∞ problem. Moreover, this sequence of feasible points is shown to converge in the sense of a weighted H 2 norm; and it does so to the solution of the H 2/H ∞ problem whenever such a solution exists.

Suggested Citation

  • G.O. Corrêa & D. M. Sales, 2003. "Transfer Function Optimization Procedure for the H 2/H ∞ Problem," Journal of Optimization Theory and Applications, Springer, vol. 116(3), pages 531-558, March.
    • Handle: RePEc:spr:joptap:v:116:y:2003:i:3:d:10.1023_a:1023013302934
    DOI: 10.1023/A:1023013302934
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