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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: IEEE Transactions on Systems, Man, and Cybernetics: Systems
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
