Networked control of discrete-time linear systems over lossy digital communication channels

Abstract

This article addresses networked control problems for linear time-invariant systems. The insertion of the digital communication network inevitably leads to packet dropout, time delay and quantisation error. Due to data rate limitations, quantisation error is not neglected. In particular, the case where the sensors and controllers are geographically separated and connected via noisy, bandwidth-limited digital communication channels is considered. A fundamental limitation on the data rate of the channel for mean-square stabilisation of the closedloop system is established. Sufficient conditions for mean-square stabilisation are derived. It is shown that there exists a quantisation, coding and control scheme to stabilise the unstable system over packet dropout communication channels if the data rate is larger than the lower bound proposed in our result. An illustrative example is given to demonstrate the effectiveness of the proposed conditions.

Commutativity of first‐order discrete‐time linear time‐varying systems

“…This example covers also the validity of the results obtained for feedback systems. Although many applications of discrete time systems are considered in various digital systems, the second example is chosen from communication area and how the benefit of commutativity for reducing noise in an amplitude modulation circuit is illustrated.…”