Stabilization of Two-Port Networked Systems with Simultaneous Uncertainties in Plant, Controller, and Communication Channels

In this paper, we study robust stabilization for the networked control system (NCS) over the communication channels described by cascaded two-port networks. Such an NCS involves simultaneous uncertainties in the plant, controller, and two-port communication channels. The cascaded two-port connections arise when signals in the NCS are transmitted through bidirectional communication channels separated by a sequence of relays. Distortions and interferences occurring in communications are taken into account. We consider {\mathcal H}-{\infty }-norm bounded uncertainties in the transmission matrices of the two-port channels, and the gap-Type uncertainties in the plant and controller models. A necessary and sufficient condition for the robust stability of the NCS is presented in the form of an 'arcsine' inequality, which states that the NCS is stable whenever the uncertainties quantified by the aforementioned metrics are well bounded and satisfy the 'arcsine' inequality. A stability margin related to the Gang of Four transfer matrix is obtained, based on which the controller synthesis problem can be solved through a special {\mathcal H}-{\infty } optimization with favorable properties. Furthermore, a generalized stability condition is studied in terms of frequency-wise bounded uncertainties, and the corresponding controller synthesis problem is proposed and solved.