System properties of Fractional Variable Order Discrete state-space system

This paper introduces the Fractional Variable Order Discrete System, described in the state space. The paper also introduces results on the controllability, reachability, observability and stability of that system. The definitions of the notions of controllability, reachability and observability for such models are proposed and the necessary and sufficient conditions for reachability and observability are given and proven. The sufficient conditions for controllability and local stability are proposed too.