Stability analysis of model-based networked distributed control systems

Networked distributed control systems (NDCSs) face serious challenges such as delays and packet dropouts induced by the communication network employed to connect local controllers of interacting subsystems. These two network-induced shortcomings may degrade the performance or even destabilize NDCSs. This paper is concerned with the problem of stability analysis and stabilization of the NDCSs, featuring both random delay and random packet loss in their communication networks. A model-based networked distributed control framework is proposed to stabilize the NDCS consisting of discrete-time subsystems interconnected through their states. In this control framework, to compensate for the adverse effects of these two network-induced shortcomings, an interaction estimator is provided in each local controller; in addition to a main control unit. This estimator uses the explicit model of the subsystems to estimate the evolution of the states of interacting subsystems, when information about their actual values is not available. A model for the NDCS subject to both random packet loss and random delay is developed. By providing a 3-step interaction estimating algorithm, the closed-loop model-based networked distributed control system (MB-NDCS) is formulated as a time-dependent impulsive system. Then, a quadratic Lyapunov function is constructed to derive a linear matrix inequality (LMI) based sufficient condition for stability analysis of the overall impulsive system. Finally, an illustrative example of a network of interconnected chemical reactors with recycle is presented to show the effectiveness of the proposed approach.