Stability and input-to-state stability for stochastic systems and applications

This paper is concerned with establishing some stability and input-to-state stability (ISS) properties in terms of two different measures, h0 and h, for nonlinear systems of stochastic differential equations of Itô type. To analyze these properties, classical Lyapunov’s method and a comparison principle are used. To justify the proposed theoretical results, applications to state estimating systems of Luenberger type and feedforward (or cascade) systems enhanced with numerical examples and simulations are presented.