2022
DOI: 10.1155/2022/5539770
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Controllability of Linear Fractional Systems with Delay in Control

Abstract: This paper discusses the controllability of continuous-time linear fractional systems with control delay. The Atangana-Baleanu fractional derivative with the Caputo approach is used. First, the solution expression for a linear fractional system is obtained. Then, the corresponding fractional delay controllability Gramian matrix is defined, and its non-singularity as necessary and sufficient conditions for the controllability is proved. Finally, another equivalent condition based on the matrix rank formed by th… Show more

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Cited by 3 publications
(3 citation statements)
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“…where operators H and L ϕ are defined by Equations ( 14) and (17), respectively. The following result holds.…”
Section: Regional Fractional Controllabilitymentioning
confidence: 99%
See 1 more Smart Citation
“…where operators H and L ϕ are defined by Equations ( 14) and (17), respectively. The following result holds.…”
Section: Regional Fractional Controllabilitymentioning
confidence: 99%
“…Due to the number of mathematical models describing dynamical systems with delays in the controls, solving controllability problems for such systems is of great importance. In particular, controllability problems for linear continuous-time fractional systems with a delayed control have been the subject of several works [15][16][17][18]. However, it should be noted that the majority of research in this area deals with the global case, that is, controllability is treated on the whole evolution domain.…”
Section: Introductionmentioning
confidence: 99%
“…Several practical applications are examined using fixed-point theory in fractional calculus as well [38][39][40][41][42]. We build on the ideas of [4,17,[43][44][45][46][47][48] in this work to examine the exponential stability for differential systems with numerous control delays and also their relative controllability, respectively.…”
Section: Introductionmentioning
confidence: 99%