Fixed/Prescribed stability criterions of stochastic system with time-delay

In this paper, the fixed/prescribed-time stability issues were considered for stochastic systems with time delay. First, some new fixed-time stability and prescribed-time stability criteria for stochastic systems with delay and multi-delay were established. Second, based on the new fixed/prescribed stability criteria, the fixed-time stabilization of the stochastic system with time-delay and the prescribed-time stabilization of the stochastic reaction-diffusion system with multi-delay were investigated, respectively. Third, two new fixed/prescribed-time delay-independent control mechanisms were designed. The primary advantage of the innovative fixed/prescribed-time controller lies in its independence from delayed states. This makes the controller applicable to systems with unknown delays. Finally, three numerical examples were provided to illustrate the feasibility of the stated theoretical results.