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Abstract

In this paper, the robust stabilization problem for a class of time-delayed multi-input systems with matched and unmatched uncertainties is considered. Here, all the matched uncertainties, unmatched uncertainties and the delay term may be time-varying. Variable structure control (VSC) is suggested to design stabilizing controllers for these uncertain time-delayed multi-input systems. The proposed controllers guarantee the global reaching condition of the sliding mode in these uncertain time-delayed multi-input systems. Further, they ensure that the system trajectories asymptotically converge to the sliding mode. In the sliding mode, the investigated time-delayed systems with matched and unmatched uncertainties still possess the insensitivity to the uncertainties and external disturbances, which is the same as the linear systems do. And the proposed controllers can work effectively for systems either with matched or unmatched uncertainties. However, the above desirable properties cannot be guaranteed by the traditional VSC design for the systems without time delays or with matched uncertainties. Finally, an illustrative example is included to demonstrate the effectiveness of the proposed variable structure controller

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