Abstract
In this research work, we investigate the controllability of linear fractional differential control systems with state and control delay. By using an explicit solution formula, a rank criterion for controllability is established. For the controllability criteria, we establish necessary and sufficient conditions of a fractional differential systems with state and control delay. In the end, a numerical example is constructed to support the results.
Highlights
The fractional differential equation is a mathematical model which is useful for the explanation of hereditary characteristics and memory of different processes and materials
A variety of research work is based on the basic study of fractional differential equations [1,2,3,4,5,6] as in further work various researchers considered control problems; for example, see [7,8,9]
Controllability is a qualitative property of fractional delay dynamical system, so one needs to find its representation of a solution
Summary
The fractional differential equation is a mathematical model which is useful for the explanation of hereditary characteristics and memory of different processes and materials. By following this study we consider a fractional differential system with state and control delay and discussed its controllability by giving its necessary and sufficient conditions. Li and Wang [27] considered pure delay for linear fractional differential equations and gave a representation of a solution by using a delayed Mittag-Leffler type matrix: cDα0+ x(t) = Ax(t – h), x(t) ∈ Rn, t ∈ J := [0, t1], h > 0, x(t) = φ(t), –h ≤ t ≤ 0, φ ∈ Ch1 := C1([–h, 0], Rn), (1)
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