Model reference control for discrete-time antilinear systems

The problem of model reference control is considered in this paper for discrete-time antilinear systems. A sufficient condition is given for the existence of an output tracking controller. It is shown that the tracking controller is a combination of a feedback stabilizing controller and a feedforward compensator. The compensation gain satisfies two matrix equations, one of which is the so-called con-Sylvester matrix equation. In addition, the feedback stabilizing gain can be obtained from a con-Sylvester matrix equation. Based on an explicit solution to the con-Sylvester matrix equation, a parametric design approach is proposed to solve the model reference control for discrete-time antilinear systems. An illustrative example is given to show the application of the proposed approach.