On the stability of the stochastic parabolic Itô equation with delay and Markovian jump

AbstractWe present a new result concerning the stability of the stochastic parabolic Itô equation subject to homogenous white noise. Our main results state that this system is exponentially stable by means of a new Lyapunov–Krasovskii functional and a linear matrix inequality (LMI). A numerical example is exploited to show the usefulness of the derived LMI-based stability