L₂−L_∞ filtering for stochastic time-varying delay systems based on the Bessel–Legendre stochastic inequality

This paper deals with the L₂−L_∞ filtering problem for stochastic systems with time-varying delay. First, based on the Bessel–Legendre inequality, a new stochastic integral inequality is established, which is called Bessel–Legendre stochastic inequality. Then, a new Lyapunov–Krasovskii functional is constructed for a stochastic time-varying delay system by utilizing Legende polynomials. With the help of the Bessel–Legendre stochastic inequality and the new Lyapunov–krasovskii functional, an L₂−L_∞ filter is developed, which can guarantee the filtering error system to be asymptotically mean-square stable with a prescribed L₂−L_∞ performance level. Finally, numerical examples are given to illustrate the effectiveness of the proposed filtering approach. The example results show that the proposed approach is less conservative than existing ones in designing the L₂−L_∞ filter for the stochastic time-delay system.