Robust Stabilization for a Logical System

This brief studies robust stabilization for a logical system under arbitrary disturbance inputs. Feedback control and pinning control design algorithms, which relying on the disturbance inputs, are developed to stabilize the logical system. In order to design feedback controller, necessary and sufficient conditions for the existence of a state feedback controller are derived. Then, constructive procedures for feedback control are provided. For the purpose of designing pinning control, an algorithm to select the pinning nodes is provided. Besides, a pinning control design algorithm is given. Finally, illustrative examples are given to show the proposed results.