Tutorial review H∞ optimal controller design for a class of distributed parameter systems

This paper is a tutorial on a frequency domain design method for the two-block H∞ optimal control of a class of SISO distributed parameter systems. Uncertainties in the system are assumed to be unmodelled dynamics represented in the form of either multiplicative, or additive, or coprime factor perturbations of a nominal infinite-dimensional plant. Performance of the closed loop system is measured in terms of the energy amplification from external input signals to the outputs of interest. In this paper transfer functions of the nominal plant and the weights are used in order to derive a solution to two-block H∞ control problems. The solution presented here uses results from operator theory. The H∞ optimal performance and controller in this method are computed from a finite set of linear equations.

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