Robust filtering of uncertain stochastic genetic regulatory networks with time-varying delays

This study is concerned with the problem of robust filtering for stochastic genetic regulatory networks with time-varying delays and parameter uncertainties. By choosing an appropriate novel Lyapunov–Krasovskii functional and establishing a new integral inequality in the stochastic setting, less conservative conditions are obtained to ensure the error systems are mean-square robustly asymptotically stable. Then the filters are designed in terms of linear matrix inequalities (LMIs) which can be checked efficiently via the LMI toolbox. What is more, the criteria can be applicable to both fast and slow time-varying delays due to our careful consideration of the ranges for the time-varying delays. Finally, two examples are presented to illustrate the effectiveness and advantages of the theoretical results.