Stabilization of linear systems with distributed input delay using reduction transformation

We propose a new stabilization method for linear systems with distributed input delay via reduction transformation and Riccati equation approach. In the presented stabilization scheme, the gain matrix of controller is constructed by the well-known linear control technique for delay-free systems. The transformation kernel matrix can be determined by solving the non-symmetric matrix Riccati equation backward with the boundary condition. When point delay systems are considered, it will be shown that the proposed control law degenerates to the standard one for input delay systems.