Asymptotic behaviour and delay-dependent H ∞ stability of nonlinear hybrid stochastic delay systems with Lévy jumps

This work investigates the stability properties of nonlinear Markovian switching stochastic differential delay equation systems (MS-SDDEs) with Lévy jumps and time-varying delays. Departing from classical linear growth condition, the coefficient functions of the system are assumed to satisfy a polynomial growth condition in a more general form. The main results of this paper are the establishment of delay-dependent criteria for H∞ and asymptotic stability through the development of an appropriate Lyapunov functional framework. Finally, a numerical example and corresponding simulation results are provided to demonstrate the validity of the theoretical analysis.