Mean-square practical stability for uncertain stochastic system with additive noise controlled by optimal feedback

Stability concepts addressed in the framework of Lyapunov are not suitable to analyze the stability of stochastic systems with additive noise since it has no equilibrium. The mean-square practical stability is introduced to study the stability of uncertain stochastic systems with additive noise controlled by linear-quadratic optimal feedback. By using Lyapunov functional methods and the comparison principle, criteria on mean-square practical stability of stochastic systems with partially known uncertainties and norm-bounded parameter uncertainties are deduced, respectively. Some numerical examples and simulations are given to illustrate the validity of the theoretical analysis.