Modeling and Output Feedback Control of Networked Control Systems with Both Time Delays; and Packet Dropouts

Li Qiu,Bugong Xu,Qin Luo,Shanbin Li

doi:10.1155/2013/609236

Abstract

This paper is concerned with the problem of modeling and output feedback controller design for a class of discrete-time networked control systems (NCSs) with time delays and packet dropouts. A Markovian jumping method is proposed to deal with random time delays and packet dropouts. Different from the previous studies on the issue, the characteristics of networked communication delays and packet dropouts can be truly reflected by the unified model; namely, both sensor-to-controller (S-C) and controller-to-actuator (C-A) time delays, and packet dropouts are modeled and their history behavior is described by multiple Markov chains. The resulting closed-loop system is described by a new Markovian jump linear system (MJLS) with Markov delays model. Based on Lyapunov stability theory and linear matrix inequality (LMI) method, sufficient conditions of the stochastic stability and output feedback controller design method for NCSs with random time delays and packet dropouts are presented. A numerical example is given to illustrate the effectiveness of the proposed method.

Highlights

Networked control systems (NCSs) are systems in which control loops are closed over a real-time communication network
We address the unified model, stability analysis, and output feedback controller design of NCSs with the sensor-to-controller (S-C) and controller-to-actuator (C-A) random time delays and packet dropouts under an Markovian jump linear system (MJLS) [43] framework
The closed-loop system (5) is a Markovian jump linear system with multiple Markov chains, which describe the behavior of the S-C and C-A time delays and packet dropouts, respectively

Summary

Introduction

Networked control systems (NCSs) are systems in which control loops are closed over a real-time communication network. The effects of packet dropouts are studied in [9,10,11,12,13,14], and of time delays in [15,16,17,18,19,20,21,22,23,24], of quantization in [7, 25,26,27,28], of time-varying transmission intervals and communication constraints in [29,30,31] and [32,33,34,35], respectively. We address the unified model, stability analysis, and output feedback controller design of NCSs with the sensor-to-controller (S-C) and controller-to-actuator (C-A) random time delays and packet dropouts under an MJLS [43] framework. The symbol ∗ within a matrix represents the symmetric entries

Problem Description

Main Results

Numerical Example

Conclusion

Proof of Theorem 5