Robust ultimately boundedness control of uncertain delayed systems under time-varying reference and external disturbance

Abstract

In the set-point following, the asymptotic property of the stability would disappear in the presence of time-varying references and disturbances. Hence, the boundedness of state variables is an essential issue in the regulation. To this aim, in light of time-varying references and disturbed signals, a robust integral policy is systematically developed to achieve the control aim in the uncertain equations with delay. Utilizing linear matrix inequality, a guideline is suggested for guaranteeing the boundedness of the solutions in uncertain systems with delays. Then, the gains of the control law are computed from a minimization. Although the boundedness is ultimately obtained in the perturbed case, the asymptotic stability would also be deduced for the nominal systems. The findings are numerically evaluated in some simulations. The favorability of the proposed integral method is shown in comparison to the traditional control strategies.

Keywords: Linear matrix inequality; Robust integral control; Time-delay systems; Ultimately boundedness.