Finite-time stability of fractional-order fuzzy cellular neural networks with time delays

Abstract The finite-time stability of fractional-order fuzzy cellular neural networks with time delays is investigated. One of the difficulties in stability analysis of fractional-order delayed systems lies in how to handle the delay terms in the systems. In view of this difficulty, firstly, a new fractional-order Gronwall inequality with time delay is developed; this can be widely used to study finite-time stability of a variety of fractional-order systems with time delays. Secondly, a new criterion for the finite-time stability of fractional-order fuzzy cellular neural networks with time delays is derived in terms of this inequality; it is less conservative than the one using the existing fractional-order Gronwall inequality with time delays. Finally, two examples are given to expound the effectiveness and less conservativeness of the proposed results.