On relay control for discrete time systems using linear matrix inequalities

Design of relay control for discrete time systems where the control is assumed to take values from a finite set of constant vectors is proposed in this paper. The stabilizability property of the plant is taken advantage of in designing a relay control which emulates locally the behaviour of a state feedback gain. A constructive method to compute the switching surfaces for the relay control and the domain of attraction is provided using linear matrix inequalities. The proposed relay feedback control design algorithm is shown to be applicable to linear parameter varying plants.