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This article addresses the problems of state bounding and state‐feedback controller design for genetic regulatory networks with multiple delays and bounded disturbances. Multiple time‐varying discrete delays and multiple constant distributed delays are involved. A delay‐dependent sufficient condition containing several simple inequalities is first given to guarantee that the state trajectories remain inside or converge exponentially into a Cartesian product of two polytopes. Furthermore, equivalent sufficient conditions directly represented by the system parameters are derived. Based on the state bounding results, one can obtain reachable set estimation and global exponential stability criteria. By designing state‐feedback controllers, the state trajectories of the close‐loop system are limited in a given Cartesian product of two polytopes. It is worthy to stress that the proposed method does not need to construct any Lyapunov–Krasovskii functional, and it can be easily realized. The effectiveness of the obtained theoretical results is illustrated by a numerical example.

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