State bounding and synthesis of switched genetic regulatory networks with mixed delays and bounded disturbances

Abstract

This paper investigates the problem of state bounding and controller design for switched genetic regulatory networks with mixed delays and bounded disturbances. A delay‐dependent sufficient condition containing several simple inequalities is first proposed to guarantee that the state trajectories remain inside or converge globally exponentially into a Cartesian product of two polytopes under the minimal dwell‐time constraint. Second, the reachable set estimation problem is further studied, and another reachable set estimation condition can be derived. Based on the reachable set estimation result, state‐feedback controllers are designed such that the state trajectories of the closed‐loop system are limited in a given Cartesian product of two polytopes. A numerical example is provided to verify the effectiveness of the obtained theoretical results.