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Local controllability of multi-term semi-linear control systems with the Caputo-type fractional difference operator

In the paper the local controllability problem of fractional multi-order and multi-step discrete-time semi-linear control systems is considered. The Caputo-type fractional order difference operator is used. The classical Kalman's controllability condition is extended to the class of fractional order multi-term linear control systems. A sufficient condition for local controllability of fractional order multi-term semi-linear control system is given.