Delta算子在不确定时延与数据包丢失下网络系统故障检测中的应用

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本研究论文深入探讨了基于观察器的网络控制系统(NCSs)故障检测问题，特别关注在存在不确定时延和数据包丢失的情况下。作者Xinyu Dong和Duanjin Zhang，来自郑州大学信息工程学院，针对这类网络系统的复杂特性提出了创新性的解决方案。网络控制系统中的不确定性主要体现在两个方面：一是时延，通常表现为随机变化且难以精确估计，被模型化为参数不确定性；二是数据包丢失，表现为非连续事件，通过伯努利分布来描述其随机性。作者运用Delta算子理论，将这些不确定性整合进一个离散模型中，以便更准确地捕捉系统的动态行为。在此基础上，论文提出了一种基于观察器的H∞故障检测滤波器。这种滤波器设计的目的是确保Delta操作系统的稳定性，并利用线性矩阵不等式(LMIs)和Lyapunov-Krasovskii函数技术，得出了滤波器稳定性和H∞性能的充分条件。通过解决这些LMIs，滤波器的参数得以优化。论文的核心贡献在于提供了一种有效的方法，可以处理不确定时延和数据包丢失带来的挑战，同时保证了网络控制系统的故障检测性能。通过仿真案例，作者展示了该方法的实际应用效果，这对于理解和改进实际网络系统的设计、故障诊断以及鲁棒控制策略具有重要意义。这篇研究论文对网络系统故障检测理论与实践的结合有深远影响，为相关领域的研究人员和工程师提供了宝贵的理论指导和技术参考。

Fault Detection for Networked Systems with Uncertain

Time-Delay and Packet Dropout using Delta Operator

Xinyu Dong, Duanjin Zhang*

School of Information Engineering, Zhengzhou University.

Zhengzhou 450001, China

E-mail: xinyudong715@163.com, djzhang@zzu.edu.cn

Abstract—This paper addresses the problem of observer-

based fault detection for networked control systems (NCSs) with

uncertain time-delays and data packet dropouts. The uncertain

time-varying delays and packet dropouts of NCSs are modeled as

parameter uncertainties of th e NCSs and a stochastic variable

satisfying Bernoulli distribution, respectively. Combining with

the delta operator theory, a new discrete model is constructed to

depict the behavior of the NCSs. Then, based on the established

model, an observer-based H



fault detection filter is proposed to

guarantee the stability of the delta operator system and the

sufficient conditions of the H



performance for the filtering error

system are derived with linear matrix inequalities (LMIs) and

Lyapunov-Krasovskii functional technique. The parameters of

the filter are solved via LMI toolbox. A simulation example is

provided to illustrate the effectiveness of the proposed method.

Keywords—networked control systems; Delta operator; fault

detection; uncertain time-delay; packet dropout; LMI

I. I

NTRODUCTION

Networked control systems (NCSs) are feedback control

systems with closed-loops via a real-time shared network,

which have several advantages such as reduced cost, simpler

maintenance and installation. Owing to NCSs’ prominent

features, more applications of them have been developed such

as automobiles control systems, intelligent building, unmanned

air vehicles and tele-surgery. However, because of the limited

of network bandwidth, the communication network also brings

some problems, such as network-induced delay, packet

dropouts and network congestion [1-2], which could degrade

the system performance and even destabilize the system.

Therefore, the research of fault detection (FD) for NCSs is of

great significance and it has attracted a great deal of attention.

In recent years, the modeling of network-induced delay and

data packet dropouts which existing in NCSs are mainly

constructed by the following methods: 1) By using Markov

random process, NCSs with uncertainties are transformed into

Markov jump linear systems(MJLS). In [3-4], Considering the

influence of the Markovian packet dropouts and the unknown

short delay which can be treated as norm-bounded

uncertainties, the NCSs were modeled as the uncertain MJLS.

References [5-6] described the phenomenon of packet dropouts

as a Markov random process. 2)The NCSs including time-

delay and packet dropout are described by the Bernoulli

distributed sequence. In [7-8], the problems of H



filtering for

NCSs with packet dropouts were discussed.

Most of these studies focused on the discrete-time systems

formulated by traditional shift operator. However, traditional

shift-operator-based methods may bring about the problems of

crowding poles located in the boundary of stability circle when

sampling is fast. With regard to high sampling rate, Goodwin

adopted delta operator instead of shift operator to discretize

continuous systems [9]. Furthermore, delta operator system has

been studied extensively due to its excellent performances [10-

13] and its practical applications have been extensively

highlighted. Nonetheless, the fault detection observer design

problem of NCSs via delta operator approach has not been

fully researched and the observer-based FD for NCSs with

uncertain time-delays and packet dropouts using delta operator

has not been investigated yet, that constitutes the main

motivation of this paper.

In this paper, the FD problems of NCSs subject to uncertain

time-delays and packet dropouts via delta operator are

investigated. The unknown networked-induced delays are

convert to the parameter uncertainties of the system. By

introducing a stochastic variable satisfying Bernoulli

distribution to describe the missing of data packet and

considering the definition of delta operator, a new delta

operator discrete system model is established. Based on the

established model and stability theory, a state observer of the

system is designed to detect faults. The sufficient conditions

for the stability of the NCSs and the existence of the FD filter

can be derived with LMI and fault observer technique.

II. D

ELTA OPERATOR SYSTEM WITH UNCERTAIN TIME-DELAY

AND PACKET DROPOUT

Consider the continuous-time linear time-invariant(LTI)

system described by

() () () () ()

() ()

xt AxtButBdtBft

yt Cxt

%% %

∀



(1)

where

()

xt R∃

is the state of the plant,

()

yt R∃

is the

measurement output,

()

ut R∃

is the control input,

()

dt R∃

is the external disturbance which belongs to

[0, ]l %

()

ft R∃

is the fault signal. Suppose that

,, , ,

ABB B C

,are

real matrices of the appropriate dimensions.

Some reasonable assumptions are given to this system:

*This work is supported by National Natural Science Foundation of China

under Grant 61471323, and the Key Program of Science Technology of

Educational Department of Henan of China under Grant 14A120004

189

978-1-4673-8644-9/16/$31.00

2016 IEEE

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