Mean-Square Finite-Time Stability and Stabilization of Impulsive Stochastic Distributed Parameter Systems

The study focuses on finite-time stability (FTS) and stabilization problems in a class of stochastic distributed parameter systems with impulsive effects. To tackle the impulsive effects within the system, we adopt two key methods: 1) a looped form quasi-periodic Lyapunov function and 2) an interpolation quasi-periodic Lyapunov function method. This combined approach allows us to obtain a detailed mean-square FTS criterion, closely related to the specific dwell time of the impulse sequence in the system. Moreover, a finite-time input controller featuring a constant gain is designed to simultaneously stabilize both the continuous and discrete components of the controlled system. Finally, we present two numerical examples to demonstrate the validity of our outcomes.