A generalized stochastic predefined-time stabilization for nonlinear stochastic systems

This paper investigates the stochastic predefined-time stabilization for nonlinear systems under relaxed stability conditions, inspired by practical control applications where intermittent energy injection and dissipation are commonly encountered. Different from existing methods that require the stochastic differential operator to be negative definite, we introduce a generalized framework that permits the combined term of the stochastic differential operator and the stability function to take arbitrary signs throughout the state space. By employing multiple Lyapunov functions and replacing the conventional pointwise negativity constraint with an integral-type condition, we derive predefined-time stability criteria that can guarantee user-defined convergence within any specified positive time bound. The theoretical framework can be adapted to three distinct cases through appropriate selection of the stability function, and we propose an explicit controller design that ensures predefined-time stabilization under mild polynomial growth conditions. The proposed methodology significantly extends the scope of predefined-time control to systems for which traditional Lyapunov-based approaches are inapplicable. Two simulation examples, including a comparative analysis demonstrating improved performance relative to existing techniques, are provided to validate the theoretical findings and highlight the practical benefits of relaxing the negative definiteness requirement.