A robust control framework for linear, time-invariant, spatially distributed systems (Q2753221)

The authors study robust control design for linear, time-invariant systems with a spatial component. The system is seen as a linear mapping from Hilbert space valued, square integrable inputs to Hilbert space valued, square integrable outputs. It is shown that these systems have a coprime factorization, which can be chosen to be normalized whenever the system is stabilizable. All definitions and results have a clear lumped parameter counterpart. For instance, it is shown that given a compensator \(C\), there exists a constant such that if the gap between the original and the perturbed plant is less than this constant, then the compensator \(C\) also stabilizes the perturbed plant. Furthermore, for any number \(b\) larger than this constant there exists a plant \(P_b\) for which the gap between \(P_b\) and the original plant equals \(b\) and \(C\) does not stabilize \(P_b\). The paper is completed with a nice design example.