A Controller Degree Bound for $\mathcal{H}^\infty $-Optimal Control Problems of the Second Kind

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Abstract
This paper is a continuation of our work on H∞-optimal control problems. In two previous articles a controller degree bound was established for problems in which both P12(s) and P21(s) are square (problems of the first kind). Here we switch our attention to problems of the second kind. We allow P12(s) to have more rows than columns (with P21(s) square), or alternatively, we allow P12(s) to have more columns than rows (with P12(s) square). Our main result shows that the degree bound derived previously for problems of the first kind carries over to problems of the second kind without change. Our analysis suggests a number of modifications which are easily made to currently available computer programs. Test calculations (for problems of the second kind) show that these improvements result in a marked reduction in computation time and also enhance the numerical robustness of the software

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