Stability analysis of networked control systems with not necessarily UGES protocols

TL;DR

This paper presents a Lyapunov-based method for analyzing the practical asymptotic stability of nonlinear networked control systems with protocols that are not necessarily UGES, using modified protocols and optimized transmission policies.

Contribution

It introduces a Lyapunov approach for stability analysis of non-UGES protocols and constructs explicit Lyapunov functions for modified Round Robin and Try-Once-Discard protocols.

Findings

Explicit Lyapunov functions for the protocols

Transmission policy avoids Zeno phenomenon

Validated with illustrative examples

Abstract

This note studies (practical) asymptotic stability of nonlinear networked control systems whose protocols are not necessarily uniformly globally exponentially stable. In particular, we propose a Lyapunov-based approach to establish (practical) asymptotic stability of the networked control systems. Considering so-called modified Round Robin and Try-Once-Discard protocols, which are only uniformly globally asymptotically stable, we explicitly construct Lyapunov functions for these two protocols, which fit our proposed setting. In order to optimize the usage of communication resource, we exploit the following transmission policy: wait for a certain minimum amount of time after the last sampling instant and then check a state-dependent criterion. When the latter condition is violated, a transmission occurs. In that way, the existence of the minimum amount of time between two consecutive transmission is established and so-called Zeno phenomenon, therefore, is avoided. Finally, illustrative examples are given to verify the effectiveness of our results.