Stability analysis for stochastic Lur’e systems with time-varying delay via some novel Lyapunov–Krasovskii functionals*

The problem of asymptotic stability is studied for a class of stochastic Lur’e systems with time-varying delay in this work. According to the characteristics of this type of systems, the suitable Lyapunov-Krasovskii functionals (LKFs) are constructed based on the dynamic delay interval (DDI) method. Then, the time-derivative of LKFs are treated by matrix inequality. According to Lyapunov stability theory, and using Schur complement, the stability criteria in terms of linear matrix inequalities (LMIs) for stochastic time-varying delay Lur’e systems are obtained. Finally, numerical example is given to illustrate the effectiveness of the criteria.