## Positive fractional discrete-time Lyapunov systems.(English)Zbl 1187.93088

Summary: Positive linear fractional discrete-time Lyapunov systems are introduced. Necessary and sufficient conditions for the positivity, reachability, controllability to zero and observability of the systems are established. Sufficient conditions for stability are given. The notion of the dual positive fractional Lyapunov system is introduced and the relationship between the reachability and observability is given. The considerations are illustrated by a numerical example.

### MSC:

 93C55 Discrete-time control/observation systems 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93B05 Controllability 26A33 Fractional derivatives and integrals