离散时间切换LPV系统故障估计：基于输入-状态稳定的方法

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本文主要探讨了离散时间切换线性参数可变系统（Discrete-Time Switched Linear Parameter Varying Systems, DTLPV）中的状态和故障估计问题，以输入-状态稳定性（Input-to-State Stability, ISS）方法为研究核心。作者是Yanzheng Zhu和Wei Xing Zheng。在许多工程领域，如自动化控制、机器人技术以及航空航天，LPV系统因其能有效建模具有非线性特性的过程而备受青睐。这些系统的特点在于其动态行为随着参数的变化而变化，这种参数的不确定性对系统的性能评估和控制策略设计提出了挑战。本文关注的是带有滞留时间约束的系统，这是一种实际应用中常见的特性，它限制了系统在不同模式之间的切换频率。为了实现对状态和故障的联合估计，作者首先假设参数变化具有多面体依赖性，这有助于分析和处理参数不确定性。他们构造了一个与滞留时间和参数相关的Lyapunov函数，这是一种在系统稳定性分析中常用的数学工具，通过Lyapunov稳定性理论来保证系统的行为在输入作用下的可控性。文章的关键贡献是建立了确保输入-状态稳定性的充分条件，这些条件满足了ISS性能要求。输入-状态稳定性是一种衡量系统对于外部输入的鲁棒性，如果能够确保ISS性能，即使存在未知的故障，系统的状态也能保持在可接受的范围内。基于此，作者采用观测器为基础的估计器来实现实时的状态和故障估计。这种方法的有效性得到了数值结果的支持，通过模拟实验验证了在实际应用中该故障估计方法的可行性和有效性。这篇研究论文针对DTLPV系统提出了一种新颖的故障估计策略，结合滞留时间和参数的特性，利用输入-状态稳定性理论，不仅实现了状态的准确估计，而且保证了在故障情况下系统的稳定性。这对于复杂系统的设计与控制具有重要的理论价值和实践意义。

Fault Estimation for Discrete-Time Switched Linear Parameter

Varying Systems: An Input-to-State Stability Approach

Yanzheng Zhu Wei Xing Zheng

Abstract— The problem of simultaneous state and fault

estimation for switched linear parameter varying systems

with dwell-time constraint is addressed in the discrete-

time domain in this paper. The polytopic dependence

property is assumed for the parameter variations. By con-

structing a suitable dwell-time-dependent and parameter-

dependent Lyapunov function, sufﬁcient conditions to

guarantee the input-to-state stability (ISS) of the aug-

mented fault estimation error system are established

to meet the ISS-gain performance requirement. Then

simultaneous estimation of the states and the faults

is implemented using an observer-based estimator. The

applicability of the developed fault estimation method is

validated by numerical results.

I. INTRODUCTION

During the past three decades, linear parameter vary-

ing (LPV) systems have gained considerable attention

in the control ﬁeld due to its attractive modeling ability

for processes with nonlinearities, since the seminal

work is carried out by Shamma in [1]. Closely linked

with the LPV systems, switched systems which involve

a conjunction between continuous dynamics and dis-

crete events have been largely concerned since they

are frequently used to model a wide range of practical

systems, see, for instance, [2], [3]. Regarding LPV

systems with a large parameter variation region, it

is rather difﬁcult to achieve satisfactory performance

requirements through a single controller. It is desired

to develop a group of LPV systems/controllers, such

that each of them corresponds to a speciﬁc parameter

subregion. Hence, a new type of systems has emerged,

This work was supported in part by the National Natural Science

Foundation of China under Grant 61603221 and the Australian

Research Council under Grant DP120104986.

Y. Zhu is with the College of Mechanical Engineering and Au-

tomation, Huaqiao University, Xiamen, Fujian, 361021, China, and

also with the School of Computing, Engineering and Mathematics,

Western Sydney University, Sydney, NSW 2751, Australia.

W. X. Zheng is with the School of Computing, Engineering

and Mathematics, Western Sydney University, Sydney, NSW 2751,

Australia.

i.e., switched LPV systems. Consequently, a large num-

ber of practical applications have been reported on the

switched LPV systems itself, and even on the switched

LPV controllers, including missile autopilot systems

[4], wind turbine [5], active magnetic bearing systems

[6], etc.

Compared with the popular average dwell time

(ADT) switching, the more general dwell time (DT)

and even persistent dwell time (PDT) switching prop-

erties have been considered frequently in recent works,

see, for instance, [9]–[13] and references therein. The

DT switching is originally used to deal with the su-

pervisory control issues referring to a family of linear

set-point controllers in [7]. To prevent the undesired

fast switching or chattering, the DT switching scheme

is employed in [8] to stabilize a linear system through

the switching control approach. In [9], the stability

and stabilization problems are addressed for a class

of linear switched systems with DT switching in the

discrete-time domain. By means of quadratic Lyapunov

functions, an upper bound of the minimal DT is de-

termined. However, it cannot directly be extended to

the issues of performance analysis and H

∞

control

containing some complex dynamics, which slows down

the research progress of switched systems under DT

switching. To overcome this issue, some advanced ap-

proaches have been explored more recently, such as the

piecewise Lyapunov function approach [10], the dwell-

time-dependent Lyapunov function approach [11], the

homogeneous rational Lyapunov function approach

[12], etc. Regrettably, in the DT switching scheme,

the corresponding analysis and control have not been

adequately done through these advanced Lyapunov

function techniques when the switched subsystem is

of LPV form.

In reality, the fault is of common occurrence in

many engineering applications, such that the practical

system suffers from loss of stability. In general, a

fault detection and estimation component is provided to

detect and estimate the fault as it occurs. A great deal of

effort has been made to cope with the fault estimation

2019 IEEE Conference on Control Technology and Applications (CCTA)

Hong Kong, China, August 19-21, 2019

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