Feedback stabilization control design for switched Boolean control networks

In this paper, the design of all possible switching signal-dependent state feedback and output feedback stabilizers for switched Boolean control networks (SBCNs) under arbitrary switching signal is investigated. By making use of the algebraic state-space approach to SBCNs, necessary and sufficient conditions for the stabilization at a given equilibrium point are presented. A new algorithm is proposed to determine all possible complete families of controllable sets for SBCNs, thereby all possible switching signal-dependent state feedback and output feedback controllers are obtained. Furthermore, we derive necessary and sufficient conditions for the solvability of the output regulation problem, and we show that, upon satisfying such conditions, also this problem can be solved by means of switching signal-dependent state feedback and output feedback controllers. At last, the proposed results are supported by examples.