Boundedness theorems of fractional-order impulsive delayed systems and its application to complex networks

Abstract

This paper focuses on the exponential ultimate boundedness of conformable fractional-order impulsive delayed systems. First, a new conformable fractional-order Halanay inequality is proposed using a method that combines the fractional-order comparison principle with the method of reductio ad absurdum. Then, by the proposed Halanay inequality and Lyapunov function method, criteria for the exponential ultimate boundedness of the systems with the convergence rate are obtained. As an application, the boundedness conditions are applied to conformable fractional-order impulsive delayed complex dynamical networks. It is noteworthy that our findings do not necessitate the decay rate to be strictly larger than the upper bound on the gain, which violates the usual boundedness conditions. This makes our results more general than existing ones. Finally, numerical examples illustrate the applicability of our findings.