| Positive systems widely exist in many fields and play an important role in them.Since the state space of a positive system is defined on a non-negative cone,rather than on the entire linear space,the research on the theory of positive systems will be more complicated than general systems.On the other hand,the security issues of network systems are becoming more and more prominent,causing widespread attention from researchers in various fields.Faced with network attacks in the network environment,the performance of the positive system will inevitably be affected.Therefore,in this paper,the controller and finite-time filter are designed for the discrete-time positive linear system with time-varying delay under the false data injection attack.Furthermore,the consensus of the discrete-time positive multi-agent system with time-varying delay under the false data injection attack is studied.The research work of this article includes the following parts:1.Dynamic output feedback control of time-delayed positive systems under false data injection attacks is studied.The time-varying time-delay and dual-channel false data injection attack model is added to the discrete-time positive linear system,and a dynamic output feedback controller is constructed.The linear co-positive Lyapunov method is used to establish a 1-gain performance index for the given positive system.On this basis,the existence conditions of the dynamic output feedback controller to be designed are determined according to the 1-gain performance index.The controller parameters are obtained through linear programming,so that the system is asymptotically stable and meets the 1-gain performance under the designed controller parameters.2.Finite-time filtering of time-delayed positive systems under false data injection attacks is studied.The time-varying delay and false data injection attack model are added to the discrete-time positive linear system,a positive full-order filter is constructed,and the concepts of finite-time boundedness and 1-gain finite-time boundedness are introduced.The finite-time boundedness analysis problem of the positive system is transformed into the finite time boundedness analysis problem of the corresponding augmented system.The linear co-positive Lyapunov method is used to obtain the sufficient conditions for the finite-time 1-gain boundness of the positive system in the form of linear programming.based on that,the design of the parameters of the finite-time positive 1-gain filter is given.3.Consensus of time-delayed positive multi-agent systems under false data injection attacks is studied.A multi-agent system with a leader is constructed in which each agent is modeled by a discrete positive linear system with time-varying delay.The communication topology of the agents is represented by an undirected graph.Considering that the agent is communicating in the process,it may suffer false data injection attack.The linear co-positive Lyapunov method is used to obtain a sufficient condition for the positive multi-agent system to achieve consensus in the form of linear programming under the designed control strategy.Based on this,a design method of control gain is proposed. |
