Asymptotical set stabilization of large-scale logical networks with stochastic delays and the application in finite-field networks

Abstract

In this paper, asymptotical set stabilization (ASS) of k-valued logical networks (KVLNs) with stochastic delays is studied by designing network-structure-based (NS-based) distributed pinning controllers (DPCs). Firstly, based on the NS-based graph method, k-valued delayed logical networks (KVDLNs) are converted into KVLNs with virtual vertices to handle the effect of stochastic delays. In addition, KVLNs with virtual vertices are transformed into the corresponding algebraic form by the semi-tensor product (STP) method. Based on the system vertices classification technique and the concept of feedback arc set (FAS), the pinning nodes set (PNS) is determined. The mode-independent and mode-dependent DPCs are designed to realize ASS of KVDLNs based on the determined PNS. Next, the obtained theoretical results are further applied to the consensus of finite-field networks (FFNs) with stochastic delays. Finally, two examples are provided to validate the theoretical results of this paper.