Maximum Allowable Delay Bound Estimation in Networked Control of Bounded Nonlinear Systems

Ashraf F Khalil,Jihong Wang

doi:10.5923/j.control.20120204.04

Abstract

Net worked Control Systems (NCSs) has been recognized as an area where theory is behind the development of technology. The defining feature of NCSs can be considered as the information is exchanged through a network among control system co mponents. So the network induced time delay is inevitable in NCSs. The time delay may degrade the performance of control systems and even destabilize the systems if they are designed without considering the effects of the time delays properly. Once the structure of a NCS is confirmed, it is essential to identify what the maximu m t ime delay is allo wed for maintaining the system stability which, in turn, is also associated with the process of controller design. Th is paper proposes a new method for estimating the maximu m allowab le time delay in networked control systems with norm bounded nonlinearity. The relation between the maximu m nonlinearity and the maximu m allowable delay is studied using the proposed method, and it is found that increasing the maximu m nonlinearity bound reduces the maximu m allo wable delay. Furthermore, increasing the time delay leads to shrink the domain of attraction. The results of the maximu m allo wable delay bound and the maximu m nonlinearity are co mpared with some of the published results.

Highlights

The advances in commun ication and network technology, and the availability of high-speed computers have resulted in an increasing interest in Netwo rked Control Systems (NCSs)
This type of control systems can be defined as a control system where the control loop is closed through a real-t ime co mmunication netwo rk[1]
The paper starts from the description of the proposed method for estimat ing the maximu m time delay for NCS with norm bounded nonlinearity

Summary

Introduction

The advances in commun ication and network technology, and the availability of high-speed computers have resulted in an increasing interest in Netwo rked Control Systems (NCSs). As the control loop is closed through a commun ication network, the time delay and data dropout are unavoidable This may degrade the performance of NCSs or even destabilize the system. The use of switching Lyapunov functional to derive stability conditions for a networked control system with bounded nonlinear uncertainty has been studied in[13]. The Lyapunov -Krasovski functional is used in[16] to derive LMI to study the stability and for designing a stabilizing controller for a networked control system with time-delay, drop-outs and bounded time-varying nonlinearity. The paper starts from the description of the proposed method for estimat ing the maximu m time delay for NCS with norm bounded nonlinearity. A few examples are illustrated, and the results are co mpared with those proposed in the previously published literature

Mathematical Analysis

Stability Analysis Case Studies

Conclusions