Finite-time stabilization of mean-field systems with uncertain parameters, multiple disturbances and delays

Abstract

The main focus of this paper is to explore the finite-time stabilization of mean-field time-varying stochastic systems that are affected by uncertain parameters, multiple disturbances, and delays. In contrast to prior studies, we present a set of sufficient conditions for achieving finite-time stability in the closed-loop model. Notably, these conditions are established based on the analysis of the state transition matrix (STM). Additionally, we address a sufficient condition based on the Lyapunov function, where the STM significantly simplifies the selection process of the Lyapunov function. Finally, we introduce a linear matrix inequality (LMI)-based approach that facilitates the computation of non-fragile controllers. The effectiveness of the developed theoretical results is verified through a stock investment model.