Output feedback sliding mode control of time delay systems with bounded disturbances

This paper considers linear time delay systems with bounded disturbances that are not necessarily matched. A static output feedback sliding mode controller is designed. The existence problem is solved by determining a sliding surface that minimizes the ultimate bound of the reduced-order dynamics in the presence of time varying delay and unmatched disturbances. Linear matrix inequalities (LMIs) are derived to compute the sliding surface via a descriptor approach. A controller that guarantees ultimate boundedness of the full-order system and ensures that the sliding surface is reached in finite time is derived using LMIs. The method facilitates sliding mode controller design for systems with polytopic uncertainties, which may appear in all blocks of the system matrices. A time delay model with polytopic uncertainties from the literature illustrates the efficiency of the proposed method and the advantages of the sliding mode controller over the linear scheme.