Global exponential stability of impulsive reaction–diffusion equation with variable delays

In this paper, the global exponential stability of an impulsive reaction–diffusion equation with variable delays is investigated. By establishing an impulsive differential inequality and using the propertied of ρρ-cone and eigenspace of the spectral radius of nonnegative matrix, some new sufficient conditions on its global exponential stability are obtained. The sufficient conditions are easily checked in practice by simple algebra methods and have a wider adaptive range. An example is given to illustrate the effectiveness of the theoretical result.