Numerical optimization for feedback stabilization of linear systems with distributed delays

This paper investigates the feedback stabilization of linear systems with distributed delays. By means of the state transition matrix (fundamental matrix) of the delay systems, an optimization problem is formulated for solving the feedback stabilization problem. We prove a necessary and sufficient condition for feedback gain matrices to stabilize the delay systems. Then a numerical method based on the condition is presented to determine the feedback gain matrices. Furthermore, numerical examples show that the presented algorithm is efficient for stabilization of the delay systems.