ABSTRACT

In this chapter, we study stabilization problems of systems governed by linear differential equations of infinite dimension. Let H be a Hilbert space equipped with inner product 〈·, ·〉 and norm ║·║. The symbol ║·║ will be also used for the ℒ(H)-norm. Our control system has state u, output y = Wu ∈ ℂ N , and input f ∈ ℂ N , and is described by a linear differential equation in H as () d u d t + L u = G f , y = W u , u ( 0 ) = u 0 ∈ H . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315367798/bad9a720-4aeb-4c28-9c18-ba1aa5ac9d9d/content/eq573.tif"/>