Controller degree bound for H∞-optimal control problems of the second kind

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.