LAUSR

In this article, by using the linear graph theory, modified algebraic Riccati equation (MARE)-based method and duality principle, two interaction protocols are proposed to achieve the scaled edge-consensus of networked discrete-time systems with unmeasurable edge-sates. Meanwhile, drawing support from MARE-based low-gain feedback technique and positive system theory, sufficient conditions are derived to ensure the bounded control inputs and positive edge-states. Moreover, feedback matrices and observer matrices are, respectively, constructed by utilizing the solutions of MARE and modified algebraic dual Riccati equation (MADRE). Remarkably, the theoretical results only use the edge number and vertex number of network rather than the global information of network. Finally, five examples are shown to demonstrate the feasibility of the interaction protocols.