Abstract
This paper addresses the robust set stabilization problem of Boolean control networks (BCNs) with impulsive effects via the semi-tensor product method. Firstly, the closed-loop system consisting of a BCN with impulsive effects and a given state feedback control is converted into an algebraic form. Secondly, based on the algebraic form, some necessary and sufficient conditions are presented for the robust set stabilization of BCNs with impulsive effects under a given state feedback control and a free-form control sequence, respectively. Thirdly, as applications, some necessary and sufficient conditions are presented for robust partial stabilization and robust output tracking of BCNs with impulsive effects, respectively. The study of two illustrative examples shows that the obtained new results are effective.
Highlights
Impulsive phenomenon is usually caused by changes in the interconnections of subsystems, sudden changes of external environment, and so on
We have studied the robust set stabilization of Boolean control network (BCN) with impulsive effects, and presented some new results
We have converted the closed-loop system consisting of a BCN with impulsive effects and a given state feedback control into an algebraic form
Summary
Impulsive phenomenon is usually caused by changes in the interconnections of subsystems, sudden changes of external environment, and so on. There exist fewer results to study robust set stabilization of BCNs with impulsive effects. In this paper, using STP, we investigate the robust set stabilization problem of BCNs with impulsive effects. (ii) Two necessary and sufficient conditions are presented for the robust set stabilization of BCNs with impulsive effects under a given state feedback control and a free-form control sequence, respectively, which are verified via MATLAB toolbox. (iii) As applications of robust set stabilization, some necessary and sufficient conditions are presented for robust partial stabilization and robust output tracking [22,23,24] of BCNs with impulsive effects.
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