Finite-time stability of impulsive reaction-diffusion systems with and without time delay

This paper considers the finite-time stability of impulsive reaction-diffusion systems (IRDSs). We deal with two cases, systems without time delay and systems with time delay. When there is no delay in the considered system, we obtain sufficient conditions to guarantee the finite-time stability of IRDSs via two representations of impulsive sequences. When time delay enters into IRDSs, we adopt a comparison method to deal with the finite-time stability and provide sufficient conditions ensuring the finite-time stability. We also present the differences of finite-time stability and asymptotic stability for the IRDSs. Moreover, in our sufficient conditions, we show the effects of impulse, diffusion and spatial domain on the finite-time stability and discuss the effect of time delay on the stability. Numerical simulations are carried out to show the effectiveness of our obtained results.