Stabilization of linear systems of infinite dimension: Dynamic feedback

In Chapter 3, stabilization problems are discussed in the framework of the static feedback scheme. While the scheme is simple, an essential assumption is that at least one of the sensorss w_k and the actuatots g_k must be constructed in a finite-dimensional subspace, that is, w_k ∈ P^*H or g_k ∈ PH, 1 ⩽ k ⩽ N. The assumption seems not plausible in engineering implementations, especially when considering the scheme of boundary observation/boundary feedback. In the case where both w_k and g_k admit spillovers, a stability improvement is discussed in Theorems 4.1 and 5.1, and also applied to the scheme of boundary observation/boundary feedback. However, the improvement is just a little. As mentioned in the beginning of Chapter 3, other recent stabilization results by static feedback scheme have serious difficulties in engineering implementation: There is little viewpoint on guaranteeing narrower supports of sensors and actuators.