Analysis and Design of Networked Control Systems with Random Markovian Delays and Uncertain Transition Probabilities

Li Qiu,Gang Xu,Fengqi Yao,Chengxiang Liu

doi:10.1155/2014/486978

Abstract

This paper focuses on the stability issue of discrete-time networked control systems with random Markovian delays and uncertain transition probabilities, wherein the random time delays exist in the sensor-to-controller and controller-to-actuator. The resulting closed-loop system is modeled as a discrete-time Markovian delays system governed by two Markov chains. Using Lyapunov stability theory, a result is established on the Markovian structure and ensured that the closed-loop system is stochastically stable. A simulation example illustrates the validity and feasibility of the results.

Highlights

Networked control systems (NCS) find many successful applications in power grids, manufacturing plants, vehicles, aircrafts, spacecrafts, remote surgery, and so on [1]
Closed-loop system (3) is a linear system with the Markovian delays d(k) and τ(k), which describe the behavior of the S-C and C-A random time delays, and with the uncertain transition probabilities
We provide the following lemma that will play a significant role in processing the uncertainty terms Δπ and Δλ of uncertain transition probability matrices πand λ

Summary

Introduction

Networked control systems (NCS) find many successful applications in power grids, manufacturing plants, vehicles, aircrafts, spacecrafts, remote surgery, and so on [1]. Most of the approaches for NCS based on Markovian jump systems framework assumed that the Markovian transition probabilities are known a priori, which severely limit the utility of the Markov model Such assumption may not hold true especially in the case where networked control is Abstract and Applied Analysis applied to the remote plants. We address the analysis and design of NCS with random time delays modeled by Markov chains in forward sensor-to-controller (S-C) and feedback controller-toactuator (C-A) communication links and with the uncertain transition probability matrices. I and 0 denote the identity matrix and zero matrix with appropriate dimensions, respectively. sym{A} denotes the expression A + AT, and ∗ means symmetric terms in symmetric entries

NCS Model

Stability Analysis and Controller Design

Numerical Example

Conclusions