Ledley Solution Method for All Feasible State Feedback Stabilizers of Boolean Control Networks With Disturbances

This paper addresses the robust stabilization problem of Boolean control networks with disturbance inputs (DBCNs) via the semi-tensor product (STP) of matrices, and designs all feasible state feedback stabilizers. Based on the algebraic form of DBCNs, some necessary and sufficient conditions are derived for the robust stabilization of DBCNs by Ledley antecedence solution technique. An algorithm is proposed to determine all complete families of robust reachable sets, moreover, all feasible state feedback stabilizers are obtained. Finally, two numerical examples are exploited to illustrate the effectiveness of the proposed results as well as the controller design scheme.