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Controllability criteria for linear fractional differential systems with state delay and impulses. (English) Zbl 1271.93028

Summary: This paper is concerned with the controllability of linear fractional differential systems with delay in state and impulses. The factors of such systems including fractional derivative, impulses, and delay are taken into account synchronously. The expression of state response for such systems is derived, and the sufficient and necessary conditions of controllability criteria are established. Both the proposed criteria and illustrative examples show that the controllability property of the linear systems is dependent neither on the order of fractional derivative, on delay nor on impulses.

MSC:

93B05 Controllability
93C05 Linear systems in control theory
34A08 Fractional ordinary differential equations
34A37 Ordinary differential equations with impulses
34K45 Functional-differential equations with impulses
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