A perfect (exact) fractional observer of discrete-time singular linear control system of fractional order is studied. Conditions for its existence are given. The obtained results are applied to the detectability problem of the class of systems under consideration.
In the paper we study the subject of stability of systems with -differences of Caputo-, Riemann-Liouville- and Grünwald-Letnikov-type with fractional orders. The equivalent descriptions of fractional -difference systems are presented. The sufficient conditions for asymptotic stability are given. Moreover, the Lyapunov direct method is used to analyze the stability of the considered systems with -orders.
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