Unbounded perturbations of the generator domain

On Perturbations of Generators ofC0-Semigroups

“…Remark 4.8. We note that in[8, Thm. 4.1] the authors study a similar problem in the context of regular linear systems.As a simple but typical example for the previous corollary we consider the space X := L p [0, 1] and the first derivativeA m := d ds with domain D(A m ) := W 1,p [0, 1] (c.f.…”

Positive semigroups and perturbations of boundary conditions

“…This is condition (2.1) of Greiner [19,Theorem 2.1]. Some extensions of this result are provided in [29] and [20] for unbounded Ψ, as well as in [1,2].…”

Approximate controllability of network systems

“…We start by the following observation on the well-posedness of the perturbed boundary control problem (34). Consideration similar to [16,Theorem 4.3] shows that the non-homogeneous Cauchy problem version of the original problem (4) is given by…”

“…[22], [30], [29], [27], [28], [25]. More precisely, using an approach presented in [16], we will first reformulate the network system as a distributed one and prove necessary and sufficient conditions for approximate controllability of such a system. More precisely, under suitable assumptions we prove that approximate controllability of such systems is equivalent to the finite dimensional Kalman-type condition, expressed only in terms of graph matrices.…”