Generalized exponential stability of stochastic delayed systems with delayed impulses and infinite delays

This paper considers the $p$th moment generalized exponential stability of impulsive stochastic delayed systems (ISDSs) influenced by both delayed impulses and infinite delays. By utilizing the Razumikhin approach, we derive new stability criteria for ISDSs. Our analysis encompasses stochastic impulsive intensities, infinite delays in continuous dynamics, and delayed impulses, without imposing constraints on their magnitudes. The proposed control strategy incorporates stabilizing impulses which ensures that the system remains stable despite impulsive disturbances occurring at specific moments. Furthermore, our criteria permit that the time derivatives of the Lyapunov function do not have upper or lower bounds, which makes them applicable to both stable and unstable original systems, as well as in scenarios where stabilizing and destabilizing impulses coexist. Additionally, the restrictions on system parameters are significantly relaxed. Finally, three illustrative examples are presented to validate the proposed results and demonstrate their practical applicability.