Receding horizon control for state delayed systems with its stability

In this paper a receding horizon control for state delayed systems is presented. The proposed controller is simple to construct and thus can be easily implemented in real applications. In deriving the proposed controller, an optimal control problem is solved to minimize control energy subject to a terminal state condition, and then the receding horizon strategy is applied to result in closed loop feedback control. To check the closed loop stability of the proposed controller, a sufficient condition is provided in terms of linear matrix inequalities. In addition, a numerical algorithm for stability checking is presented to compute the eigenvalues of state delayed systems, which can be applied to general distributed delay systems with noncommensurable multiple delays.