Observability, time-varying stability and feedback control of discrete-time antilinear systems

This paper investigates some properties of discrete-time antilinear systems. The observability of this kind system is examined by the certain gram matrix. As to the time-varying stability of the discrete- time anti-linear system, a time-varying discrete anti-Lyapunov equation is proposed for actual operation. Meanwhile, the observability, and the controllability of feedback control are expressed by the discriminant matrices for the time-invariant case. All the theorems are proved by rigorous mathematical expressions.