On exponential stability in mean square of nonlinear delay differential equations with Markovian switching

This paper addresses the exponential stability of nonlinear delay differential equations with Markovian switching. Drawing upon the comparison principle, we introduce the explicit criteria for achieving the exponential stability in mean square (sense). These criteria are formulated in terms of the equation coefficients and the generator of the Markovian switching process. As a result, these criteria can be verified without needing to construct the Lyapunov functions, a departure from the conventional approach found in the Razumikhin-type theorems. The paper includes an illustrative example and also demonstrates an application to the switched neural networks.