Finite-time adaptive stability of gene regulatory networks

Abstract

This paper is concerned with the finite-time adaptive stability of genetic regulatory networks(GRNs). Traditionally, the finite-time stability criterion is often established based on the prior information on gene regulatory parameters. However, it is difficult to acquire the above prior information for GRNs. To overcome the above difficulty, we design controllers in non-switching and switching gene regulatory networks with adaptive technique, respectively. Then, we derive a sufficient criterion for system to achieve finite-time stability under the action of an adaptive controller and give an estimate of the steady-state time. Furthermore, we can also shorten the setting time required for the system to achieve finite-time stability under the designed adaptive controller. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design method.