Networked Robust Stability for LTV Systems with Simultaneous Uncertainties in Plant, Controller, and Communication Channels

In this paper, we study the robust stability of a networked control system (NCS) under the framework of infinite-dimensional discrete-time linear time-varying (LTV) systems. The NCS consists of a pair of uncertain plant and controller, as well as an uncertain bilateral communication channel in between. The uncertainties in the plant and controller are measured by the gap metric. The communication channel between the plant and controller is described by a cascade of two-port networks whose transmission matrices are subject to norm-bounded additive uncertainties. Such an uncertain two-port network can model distortions and interferences occurring during control and measurement signal transmissions. The causality of the LTV subsystems is characterized by using nest algebras. A necessary and sufficient condition for the robust stability of the NCS, with the causality of all system components explicitly considered, is established in the form of an arcsine inequality which generalizes a similar result for linear time-invariant NCSs.