Robust Stability and Stabilisation of Delayed Boolean Networks With Disturbance

Abstract

In this paper, we study a type of delayed Boolean networks(DBNs) which are affected by disturbances. We study the stability problems of this kind of DBNs based on algebraic form, which can be constructed by the semi-tensor product(STP) method. Firstly, the robust stability of DBNs without control is investigated, and the decision condition for robust stability is derived. Then, the robust stabilisation and control design problems are considered. Based on the algebraic representation of the delayed Boolean control networks(DBCNs), a necessary and sufficient condition is established to judge the robust stabilisation of the system, moreover, a state feedback control is also designed to robustly stabilize the DBCNs. Finally, we give an example to support our new results.

Keywords

• DBNs
• robust stability
• robust stabilisation
• disturbance inputs
• STP