Controllability and observability of switched Boolean control networks

Topological structure and the disturbance decoupling problem of singular Boolean networks

“…In the following, we will discuss the solvability property of SBN (13). According to Lemma 2, if there are two columns of E: (13) is not unique for some initial value.…”

“…For an initial value x(0) = δ i0 2 n , we have Ex(1) = Col i0 (F). Then, Col i0 (F) must in Col(E), otherwise the solution of SBN (13) does not exist. In order to ensure the solution is unique, there cannot be two different elements x 1 , x 2 in the admissible condition set such that Ex 1 = Ex 2 .…”

“…STP is an effective tool, because it can convert a Boolean network into a standard discrete-time system [5,6]. Many problems of Boolean networks, such as realisation problem [7], stability and stabilisation problems [6], identification problem [8], controllability and observability [9][10][11][12][13], have been easily solved by STP approach. Moreover, Cheng [14] has also studied the disturbance decoupling problem (DDP) of Boolean control networks, which is another fundamental problem.…”

Observability analysis and observer design for finite automata via matrix approach

“…Based on semi-tensor product (STP) of matrices developed by Cheng [18], the observability problem of Boolean networks, which can be seen as a special case of automata driven by logical relations between states, were considered in [19][20][21][22][23][24]. In spite of these existing results, necessary and sufficient conditions that are readily verifiable for different observability concepts of finite automata are still in need.…”

Complete synchronisation for two coupled logical systems

“…In addition to naturally occurred switchings, switched dynamics can be the results of external intervention that attempts to re-engineer a given network by turning on and off. Hence, it is natural to present a switched Boolean network (SBN), where its dynamic is governed by different SBNs [16][17][18]. The synchronisation of SBNs is meaningful too.…”