Stability of impulsive delayed switched systems with conformable fractional-order derivatives

In this paper, exponential stability is addressed for impulsive delayed switched systems with conformable derivatives by Halanay inequalities technique. First, based on the fractional-order monotonicity theorem and the definition of conformable fractional-order derivative, novel conformable fractional-order Halanay inequalities are developed that extend and improve the existing ones. Second, using the obtained Halanay inequalities and the estimate of conformable fractional-order exponential functions, globally exponential stability conditions that depend on the infimum and supremum of impulsive step sizes are proposed for the systems. Third, more relaxing stability conditions are presented that do not depend on the infimum and supremum of impulsive step sizes, which means that the conditions on impulses are weaker than those commonly used in the existing literature. Finally, examples are given to illustrate the validity of the theoretical results.