Design of H∞ three-delay controllers for systems with time delay

The method of designing the H_∞ three-delay controllers for systems with time delay is investigated in this paper. The advantages of the controllers based on the delay modules lie in that it is easy to implement and it can be implemented in the occasions that ordinary controllers cannot be implemented. The three delay modules introduced into the controller is to improve the performance of the controlled system. Based on the complementary sensitivity function, the parameters of the three-delay controller are optimized with H_∞ performance. Then, the problem of finding the set of the H_∞ three-delay control parameters satisfying the certain H_∞ performance is converted to the problem of stabilizing the quasi-polynomials which can be solved by using the D-composition method. Finally, the set of the three-delay control parameters is derived by finding the intersection of stable region and H_∞ region. The simulation results verify the effectiveness of the proposed method.