Controllability and stability of discrete-time antilinear systems

In this paper, the discrete-time antilinear systems are investigated. Firstly, a closed-form expression for the state response of discrete-time antilinear systems is established. Secondly, the concepts of reachability and controllability are proposed for discrete-time antilinear systems. With the closed-form expression of the state reponse as tools, anti-Gram criteria for reachability are given. In addition, a matrix rank criteria for reachability and controllability is given for time-invariant antilinear systems. In addition, an anti-Lyapnov equation approach is given to check the stability of the time-invariant antilinear systems.