Consensus Analysis And Control Of Finite Field Networks With Time Delays

Finite field networks(FFNs)are a kind of networked control systems modelled in finite field,which have wide applications in many research fields such as wireless sensor networks.FFNs are suitable for network environment with capacity,memory and time constraints.Using the algebraic state space approach and the networked control system theory,this paper st.udies the consensus analysis and control issues of FFNs with time delays,including leader-follower consensus,consensus of FFNs with switching topology and robust set stabilization.Firstly,the semi-tensor product of matrices method is used to convert the leader-follower FFNs with time delays into a linear form,and the state-based leader-follower FFNs with time delays is con-verted into a trajectory-based leader-follower FFNs with time delays through the state expansion.Both forms are proved to be equivalent with respect to the issues studied,which facilitate t.he use of classical control theory to study the FFNs with time delays.Secondly,the concepts of consensus and consensus with probability one over FFNs are defined,and two kinds of stochastic time delays are formulated,that is,probabilistic time delays and Markov jump time delays.Based on the equiva-lent algebraic form of FFNs,some necessary and sufficient conditions are presented for the consensus of leader-follower FFNs with constant time delay,stochastic time and switching topology,respectively.Finally,an event-triggered control scheme is proposed and the robust set stabilization of logical control networks is studied.By defining a series of reachable sets,the necessary and sufficient conditions for robust set stabilization are presented and a constructive procedure is proposed to design the corresponding state feedback event-triggered controllers.Some illustrative ex-amples are given to support the obtain new results.