Mean-square practical stability criteria for uncertain time-varying stochastic systems with additive noise controlled by optimal feedback

The fact that stochastic systems with additive noise do not have any equilibrium makes stability concepts addressed in the framework of Lyapunov are not suitable to analyze the stability of such systems. The mean-square practical stability is introduced to study the stability of uncertain time-varying stochastic systems with additive noise controlled by optimal feedback in this paper. By using Lyapunov functional methods and the comparison principle, criterion on mean-square practical stability of such system is deduced. Numerical example and simulation are given to illustrate the validity of the theoretical analysis.