Mean-square finite and prescribed-time stability for nonlinear stochastic parabolic distributed parameter systems☆

In this paper, the mean-square finite-time stability (MSFTS) and mean-square prescribed-time stability (MSPTS) of a class of nonlinear stochastic parabolic distributed parameter systems are studied. An internal dynamic variable is introduced to design dynamic periodic event- triggered mechanism (DPETM) for FTS. Moreover, a new prescribed-time DPETM is proposed by combining two different adjustment functions to reduce the update frequency of the controller. Based on designing distributed controllers, the sufficient conditions for the closed-loop system's MSFTS and MSPTS are provided in the form of linear matrix inequalities (LMIs), respectively. Here, the Lyapunov-Krasovskii functional method, integral inequality, and L'Hospital's rule are used. Finally, two numerical examples verify the effectiveness of the proposed finite-time and prescribed-time control algorithms.