Asynchronous Control of Stochastic Switched Boolean Control Networks With Piecewise-Homogeneous Dwell Time

In this article, the l₁-induced performance of the stochastic switched Boolean control network (BCN) is investigated. The switched signal is considered to follow a time-varying probability distribution, the switching of which is considered to have a random dwell time. The asynchronous state feedback control (SFC) is studied to achieve the control objective. This kind of control can avoid the failure of the control due to the inconsistency between the system mode and the control mode, so the results obtained are more general. Using the semitensor product of matrices, the algebraic form of the considered BCN is represented. Under this framework, sufficient conditions are obtained to ensure that the closed-loop system is stochastic stabilized with a prescribed l₁-induced performance level ɣ. Parameters can be solved by inequalities. In addition, when the dwell time converges to infinity, the probability distribution of the switched signal becomes fixed. Necessary and sufficient conditions are presented to ensure the stabilization of the closed system under asynchronous SFC as well as the design of the asynchronous SFC. Then, sufficient condition is obtained for the prescribed l₁-induced performance level. Examples are presented to show the effectiveness of the obtained results.