Set stability of switched delayed logical networks with application to finite-field consensus

摘要

This paper investigates the set stability of switched delayed logical networks (SDLNs) by using the semi-tensor product of matrices. The equivalent algebraic form of SDLNs is established, and it is proved that the set stability of SDLNs is equivalent to the set stability of the algebraic form with respect to trajectory. Based on the switching point reachability, a necessary and sufficient condition is proposed for the set stability of the algebraic form, which is also the criterion for the set stability of SDLNs. The obtained results on the set stability of SDLNs are applied to the consensus of finite-field networks (FFNs) with switching topology and time delays, and a new necessary and sufficient condition is presented for the finite-field consensus. (C) 2019 Elsevier Ltd. All rights reserved.