On the Computation of Suboptimal H∞ Controllers for Unstable Infinite Dimensional Systems
In this paper we show how to compute suboptimal H ∞ controllers, for a class of (possibly) unstable and (possibly) infinite dimensional plants, from a finite set of linear equations. A solution to the H ∞ suboptimal control problem for infinite dimensional stable plants was obtained in . Also, in  and  the H ∞ optimal control problem was solved for unstable distributed plants. Our solution for the suboptimal control problem of unstable distributed plants is based on the techniques developed in  and . We obtain a computable expression for the suboptimal H ∞ controllers and identify their finite and infinite dimensional parts.
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- D.S. Flamm, Outer Factor ‘Absorption’ for H ∞ Control Problems, ISS Report No. 55, July 31, 1990, Dept. of Elec. Eng., Princeton University, 1990.Google Scholar
- C. Foias, H. Ozbay and A. Tannenbaum, Remarks on H ∞ optimization of multi-vari ate distributed systems, IEEE Conference on Decision and Control, Austin, Texas, December 1988, pp. 985–986.Google Scholar
- C. Foias and A. Tannenbaum, On the parametrization of the suboptimal solutions in generalized interpolation, Linear Algebra and its Applications, 122/123/124 (1989), pp. 145–164.Google Scholar
- H. Ozbay, M.C. Smith and A. Tannenbaum, Mixed sensitivity optimization for a class of unstable infinite dimensional systems, (to appear in) Linear Algebra and its Applications. (A short version of the paper, tinder the title Controller design for unstable distributed plants, appears in the Proc. of the American Control Conference, San Diego CA, May 1990, pp. 1583–1588.Google Scholar
- H. Ozbay, M.C. Smith and A. Tannenbaum, On the optimal two block H ∞ compensators for distributed unstable plants, Proceedings of the American Control Conference, Chicago IL, June 1992, pp. 1865–1869.Google Scholar
- M.C. Smith, On stabilization and existence of coprime factorizations, IEEE Transactions on Automatic Control, 1989, pp. 1005–1007.Google Scholar
- H. Tu, An H ∞ Optimization Method and Matlab Program for Linear Distributed Systems, M.S. Thesis, University of Minnesota-Duluth, 1992.Google Scholar