Reference Tracking for Linear Time Invariant Systems with a Relay Control

This paper investigates the problem of tracking a reference trajectory for Linear Time Invariant (LTI) systems using a relay feedback. First of all, the problem of a reference tracking is reformulated as a stabilization problem of the tracking error. Then, under some conditions on the reference inputs a design approach of a relay feedback controller that guarantees a perfect tracking of the reference trajectory is provided. Moreover, conditions in LMI form are proposed in order to synthesize a relay feedback and provide an estimation of the domain of attraction. Secondly, the case where the reference inputs can take the same values as the control input is considered. In this context, achieving a perfect tracking is no longer possible. Thus, using the comparison principle, a relay feedback controller that guarantees a practical stabilization of the tracking error is proposed. An estimation of the domain of attraction along with the bound of the tracking error are equally provided. Finally, computer simulations show the efficiency of the developed method over a numerical example.