State feedback control for fractional differential equation system in the space of linearly correlated fuzzy numbers

In this paper, we will introduce Caputo fractional LC derivative defined in the linear correlated fuzzy-valued number space RF(A) and some of its applications, specifically the feedback control problem in the space RF(A) in the sense of Caputo fractional LC derivative. Firstly, we give definition of the Riemann-Liouville-LC integral and the Caputo fractional LC derivative of a function that takes value in RF(A). Besides, some Caputo factional LC derivative properties of the sum and difference of two functions have also been proved. Moreover, the problem of dynamic systems in space RF(A) is given in both cases where A is a symmetric or non-symmetric fuzzy number. Along with that, the stability theorems of the equilibrium point are also taken into consideration. Finally, we are interested in building a state feedback control function for the fractional differential equation system in space RF(A) to ensure the equilibrium point of the system is asymptotically stable. (c) 2022 Elsevier B.V. All rights reserved.