  We propose an SDP-based framework to address the stabilization of input delay
systems while taking into account dissipative constraints. A key to our
approach is the introduction of the concept of parameterized linear dynamical
state feedbacks (LDSFs), which draws inspiration from recent advancements in
the analyses of distributed delays. Importantly, the parameterized LDSFs
generalize conventional predictor controllers, where the interpretation of
state prediction is concealed and their degree of parameterization can be
increased by adjusting the integral kernels. A sufficient condition for the
existence of dissipative LDSFs is formulated as matrix inequalities by
constructing a complete type Krasovski\u{\i} functional. To solve the bilinear
matrix inequality in the synthesis condition, we employ an off-line inner
convex approximation algorithm that can be initialized using the gains of
predictor controllers obtained via explicit construction. Finally, the unknowns
of our dissipative LTDS can be directly obtained by solving convex semidefinite
programs. Numerical examples and simulations were experimented to demonstrate
the validity and effectiveness of our methodology.
