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A method is given for solving an optimal H2 approximation problem for SISOlinear time-invariant stable systems. The method, based on constructivealgebra, guarantees that the global optimum is found; it does not involve anygradient-based search, and hence avoids the usual problems of local minima. Weexamine mostly the case when the model order is reduced by one, and when theoriginal system has distinct poles. This case exhibits special structure whichallows us to provide a complete solution. The problem is converted into linearalgebra by exhibiting a finite-dimensional basis for a certain space, and canthen be solved by eigenvalue calculations, following the methods developed byStetter and Moeller. The use of Buchberger's algorithm is avoided by writingthe first-order optimality conditions in a special form, from which a Groebnerbasis is immediately available. Compared with our previous work the methodpresented here has much smaller time and memory requirements, and can thereforebe applied to systems of significantly higher McMillan degree. In addition,some hypotheses which were required in the previous work have been removed.Some examples are included.

Optimal H2 order-one reduction by solving eigenproblems for polynomial equations