Controllability results for nonlinear higher order fractional delay dynamical systems with control delay. (English) Zbl 1418.93037
Summary: This paper establishes a set of sufficient conditions for the nonlinear fractional delay dynamical systems with control delay of order \(1<\alpha<2\), and the delays are in state variable as well as control variable. The solution representations are provided. The main tool are the Mittag-Leffler matrix function and the Schaefer’s fixed point theorem. Examples are presented to illustrate the results.
MSC:
| 93B05 | Controllability |
| 93C10 | Nonlinear systems in control theory |
| 34A08 | Fractional ordinary differential equations |
| 93C23 | Control/observation systems governed by functional-differential equations |
Keywords:
controllability; fractional delay differential equation; Laplace transform; Mittag-Leffler matrix function; Schaefer’s fixed point theoremReferences:
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