STABILIZATION OF BOOLEAN CONTROL NETWORKS UNDER APERIODIC SAMPLED-DATA CONTROL

A novel technique is provided for the global stability analysis of Boolean control networks (BCNs) under aperiodic sampled-data control (ASDC). The sampling period is allowed to be taken from a limited number of values. Using the semitensor product of matrices, a BCN under ASDC can be converted into a switched Boolean network (BN). Here, the switched BN can only switch at sampling instants, which does not mean that the switches occur at each sampling instant. For the switched BN, we consider two cases: (i) switched BN with all stable subsystems; (ii) switched BN containing both stable subsystems and unstable subsystems. For these two cases, the techniques of switching-based Lyapunov function and the average dwell time method are used to derive sufcient conditions for global stability of BCNs under ASDC, respectively. The upper bounds of the cost function, which is defned to guarantee that the considered BCN is not only globally stabilized but also can assurance the performance at an appropriate level, are determined, respectively. Moreover, an algorithm is presented to construct the ASDCs. Finally, the obtained results are demonstrated by several examples.