Controllability Criteria for Type-۲ Fuzzy Fractional-order Dynamical System via Mittag-Leffler Matrix Function using granular derivative.

This study is concerned with finding the controllability of granular type-۲fuzzy fractional-order dynamical control systems (GrT۲FuFDCS) usingMittag-Leffler matrix function. Some new concepts concerning to granularinterval valued type-۲ fuzzy fractional derivative is introduced inthis paper. To arrive at finding the controllability of the type-۲ fuzzydynamical system, type-۲ triangular fuzzy function and type-۲ triangularfuzzy numbers are used to model fractional dynamical controlsystem. Besides, the controllability Grammian matrix is defined basedon Mittag-Leffler matrix function. Granular fuzzy Laplace transform andinverse Laplace transform are utilized to derive the solution of the type-۲ triangular fuzzy fractional-order control systems. The derived resultsensure that the controllability of the proposed GrT۲FuFDCS for bothlinear and non-linear case exists. Finally, numerical examples and theirsimulation results are given to illustrate the merit of the obtained results.

کلیدواژه ها:

Horizontal membership function ، Type-۲ triangular fuzzy number ، Type-۲ fuzzy granular Laplace transform ، Type-۲ fuzzy fractional differential equations ، Granular differentiability ، Granular fuzzy fractional derivative ، Type-۲ fuzzy fractional granular controllability