Robust optimization of distributed parameter systems

In this paper, we will discuss the use of new methods from robust control and especially H°° theory for the explicit construction optimal feedback compensators for several practical distributed parameter systems. Indeed, based on operator and interpolation theoretic methods one can now solve the standard H control problem for a broad class of systems modelled by PDEs. In our approach, the complexity of the computations involved is only a function of the weighting filters, and not the state space dimension which is why we can handle infinite dimensional systems with no approximations involved. These techniques are based on certain operator theoretic notions connected with a class of operators which we call skew Toeplilz. These are precisely the operators which appear in the H°° optimization problem.