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

Przyborowski, Przemysław

Arch. Control Sci. 18, No. 1, 121-134 (2008).

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

Keywords:

fractional; positive; discrete-time; Lyapunov system; stability; controllability to zero; reachability