Time-optimal state feedback stabilization of switched Boolean control networks

This paper investigates the time-optimal state-feedback stabilization of switched Boolean control networks (SBCNs). Based on the properties of the semi-tensor product (STP) of matrices, a technique is proposed to merge the switching signal and all inputs of subnetworks into a single input variable. This technique allows us to transfer a SBCN to an equivalent non-switching logical control network (LCN) and eases the analysis and design process significantly. So long as a state-feedback stabilizer is obtained for the resulting non-switching LCN, it can then be decomposed uniquely into the respective state feedbacks of the sub-networks and the state-dependent switching law. Based on this technique, the controllability and stabilisability of such SBCNs are solved and an algorithm for finding all time-optimal switching state feedbacks is proposed. An example is described to illustrate the main results and the design process proposed in this paper.