Asymptotical Mean-Square Stabilization of Networked Control Systems Operating Over Multipath Routing Networks

In this article, we mainly study an integrated networked control system operating over multipath routing networks, where the delivered control signal in each path experiences both transmission delay and packet loss. These imperfections significantly compromise system performance and may even cause instability. For such a system, we derive, for the first time, the necessary and sufficient stabilization condition utilizing a delay-dependent algebraic Riccati equation. Different from many previous works, one significant contribution is that our control policy is designed as the feedback of an extended state that contains the current available state and relevant past control information. Furthermore, we introduce an existence and uniqueness theorem for the maximum packet loss rate in symmetric systems. Notably, we derive its closed-form expression specifically in the scalar case.