H∞-optimal mixed sensitivity for general distributed plants

The authors show how the results and techniques presented by G. Zames and S. Mitter (Syst. & Control Let., vol. 10, pp. 159-165, 1988) can be extended to a very general single-input/single output (SISO) mixed sensitivity problem, in which the transfer function of the plant to be controlled has both irrational stable and irrational unstable parts. It is shown, as an extension of F. Fagnani´s work (1987), how to transform the scalar mixed sensitivity problem into the ´standard form´ which is the starting point from which Zames and Mitter computed the optimal norm of the mixed sensitivity. This transformation allows some new observations about this problem that have design significance. These developments are motivated by the computation of the infimal H^∞-norm of the mixed sensitivity for the irrational transfer function model developed by D.S. Flamm (ISS Report No. 54, June 14, 1990, Dept. of Electr. Eng., Princeton Univ.)