Linear matrix inequality-based repetitive controller design for linear systems with time-varying input delay

This style deals with the problem of delay-dependent stability criterion and repetitive controller design for linear systems with time-varying input delay. First, based on the existing literature, a rate-dependent state feedback controller is designed so that the closed-loop system is stabilised and the effect of disturbances is reduced to an ideal level. Second, by combining the state vectors of the stabilised system and repetitive controller, a delay-dependent stability criterion is derived in the form of linear matrix inequality (LMI) for the augmented system. Third, by reformulating the LMIs given in the stability criterion, the design problem of the repetitive controller is transformed to an optimisation problem subject to LMI constraints. Two simulation examples are provided to illustrate the validity of the proposed method.