An LMI approach to the control of exponentially unstable systems with input time delay

The stabilization of exponentially unstable linear systems with time-varying input delay is revisited in this paper. The proposed stabilizing controller for input delayed systems with poles in the open right-half plane is obtained from the iterative solution to two LMI problems. First, the upper bound of the delay function is considered to be a known parameter, and a stabilizing controller is found from the feasible solution of an iterative LMI problem. Second, the stabilizing controller is obtained from the optimal solution to an iterative LMI problem, such that the upper bound of the delay function is maximized. The effectiveness of the proposed methods is demonstrated through numerical examples, and by experimental testing on a balanced beam test rig.