Optimal H2 Model Reduction in State-space: a Case Study

A state-space approach to H2 model reduction of stable systems is pursued, using techniques from global rational optimization, and aimed at finding global optima. First, a concentrated version of the H2 criterion is derived, by optimizing analytically with respect to a subset of parameters. Next, a bound is developed, which is shown to be sharp for reduction to models of order 1. The choice of parameterization is such as to keep all these criteria rational. To illustrate the approach, a nontrivial example of a multivariable stable system of order 4 was designed, together with an approximation of order 2. Detailed analysis shows the approximation to be the global optimum among all stable system of order 2, constituting the first such system described in the literature. The fact that it also yields a global optimum to the bound, which happens to be sharp at the optimum, leads to a couple of questions for further research.