  In this note, we present an effective solution to the stabilization of linear
input delay systems subject to dissipative constraints while all the effect of
input delay is compensated by a controller with novel structure. The method is
inspired by the recent development in the mathematical treatment of distributed
delays and predictor controllers, which are critical for the derivation of the
solution. An important conceptual innovation is the use of a parameterized
dynamical state feedback controller (DSFC), where the dimension of the
controller equals the dimension of the control input. A sufficient condition
for the existence of a dissipative DSFC is obtained via the Krasovskii
functional approach, where the condition includes a bilinear matrix inequality
(BMI). To solve the BMI, we apply an inner convex approximation algorithm which
can be initialized based on an explicit construction of a predictor controller
gain. The proposed DSFC can be considered as an extension of the classical
predictor controller, thereby capable of compensating all the effects of the
pointwise input delay while satisfying dissipative constraints. A numerical
example is given to illustrate the effectiveness of our proposed methodology.
