Stabilization for distributed semilinear systems governed by optimal feedback control

Weak and strong stabilization for time-delay semi-linear systems governed by constrained feedback control

“…2. If r = 0, we obtain the same results retrieved as in [6] for infinite dimensional semi-linear systems.…”

“…Next, we will establish the estimate (6). By using the variation of constants formula (11) and taking z(t) = y(t) − S(t)y(0), ∀t 0, one can get that…”

“…The stabilization problem for distributed semi-linear systems without delay (i.e., for r = 0) has been studied in many works, (see e.g. [1,4,6]). In [1], it has been shown that if N is weakly sequentially continuous, then the weak stabilization result has been established using the following quadratic feedback control: v 0 (t) = − N y(t), y(t) provided that N S(t)φ, S(t)φ = 0, ∀t 0 =⇒ φ = 0, ∀φ ∈ H…”

“…In [6], the authors had used the following feedback control to show that it guaranteed the weak and strong stabilization to the system (1) without delay:…”