Exponential L 2 - L ∞ Filtering for a Class of Stochastic System with Mixed Delays and Nonlinear Perturbations

Abstract

The delay-dependent exponential $L_2\text{-}{L}_{\infty }$ performance analysis and filter design are investigated for stochastic systems with mixed delays and nonlinear perturbations. Based on the delay partitioning and integral partitioning technique, an improved delay-dependent sufficient condition for the existence of the $L_2\text{-}{L}_{\infty }$ filter is established, by choosing an appropriate Lyapunov-Krasovskii functional and constructing a new integral inequality. The full-order filter design approaches are obtained in terms of linear matrix inequalities (LMIs). By solving the LMIs and using matrix decomposition, the desired filter gains can be obtained, which ensure that the filter error system is exponentially stable with a prescribed $L_2\text{-}{L}_{\infty }$ performance $\gamma$. Numerical examples are provided to illustrate the effectiveness and significant improvement of the proposed method.