Prescribed-time stability of stochastic nonlinear delay systems

Abstract

This paper investigates the prescribed-time stability and stabilization problem for stochastic nonlinear delay systems. We introduce a new definition of prescribed-time mean-square stability which includes stability in probability and prescribed-time convergence to zero. Utilizing the prescribed-time adjustment function and some stochastic analysis techniques, we establish Lyapunov theorems of prescribed-time mean-square stability for stochastic nonlinear delay systems. An appealing feature of the new theorems is that the solution of prescribed-time stable stochastic nonlinear delay systems can converge to zero at any preset time irrespective of initial data and design parameters. Moreover, under the local Lipschitz condition and the Khasminskii-type condition, we prove that the controlled stochastic nonlinear delay system has a unique solution and achieves prescribed-time mean-square stability. Two simulation examples demonstrate the effectiveness of the theoretical analysis.