State Bounding Description and Reachable Set Estimation for Discrete-Time Genetic Regulatory Networks With Time-Varying Delays and Bounded Disturbances
Yu Xue, Chunyan Liu, Xian Zhang
Abstract
This article investigates the problems of state bounding description and reachable set estimation for discrete-time delayed genetic regulatory networks with bounded disturbances. A novel delay-dependent sufficient condition composing several simple linear matrix inequalities is first given to guarantee that the state trajectories converge globally exponentially into a Cartesian product of two polytopes. Furthermore, equivalent sufficient conditions directly represented by the system parameters are derived. As applications, it is shown that these sufficient conditions are exactly global exponential stability criteria of the zero equilibrium when the disturbances vanish, and the Cartesian product of two polytopes can be viewed as a reachable set estimation of the states when the initial functions are limited into a certain range. The effectiveness of the proposed approach is illustrated by two numerical examples. Compared with the existing results, it is worthy to stress that the presented method does not need to construct any Lyapunov–Krasovskii functional and can be easily realized.