Maiying Zhong

Fault diagnosis of networked control systems

Networked control systems (NCS) are feedback systems closed through data networks. NCS have many advantages compared with traditional systems; however, the network-induced delay and other characteristics of data networks may degrade the performance of feedback systems designed without taking the network into account. Supported by the National Nature Science Foundation of China, we studied the fault diagnosis and fault-tolerant control theory for NCS in recent years. This paper summarizes our main ideas and results on fault diagnosis of NCS, including the fundamentals of fault diagnosis for NCS with information-scheduling, fault diagnosis approaches based on the simplified time-delay system models, and the quasi T–S fuzzy model and fault diagnosis for linear and nonlinear NCS with long delay. # 2007 Elsevier Ltd. All rights reserved.

New Exponential Estimates for Time-Delay Systems

This note considers the problem of exponential stability for time-delay systems. In terms of linear matrix inequalities, a new sufficient condition for exponential stability is obtained. Based on this, an improved upper bound of the decay rate can be easily calculated. When time-varying norm-bounded parameter uncertainties appear, a new sufficient condition for robust exponential stability of uncertain time-delay systems is also provided. The reduced conservatism of the proposed conditions is illustrated via two numerical examples

On Designing

This technical note deals with the problem of finite horizon H∞ fault detection for linear discrete time-varying systems. Using an observer-based fault detection filter (FDF) with residual feedback as a residual generator, a new problem formulation of fault detection is first presented. Then the design of finite horizon H∞ -FDF is converted into a minimum problem of certain quadratic form. Through building a relationship with Krein space projection and applying innovation analysis, a sufficient and necessary condition for the minimum is derived and a solution to the H∞ -FDF is obtained by recursively computing Riccai recursions. Numerical examples are given to show the effectiveness of the proposed method.

H_{\infty}

This note deals with the problem of observer-based fast rate fault detection for a class of multirate sampled-data (MSD) systems. Applying a lifting technique, a linear time-invariant (LTI) representation with slow sampling period is firstly obtained for the MSD systems and, based on this, an observer-based fault detection filter is considered as a residual generator. Then an optimization fault detection approach for LTI systems is modified to the residual generation for the MSD systems and, by solving a discrete-time Algebraic Riccati equation, a family of optimal solutions with causality constraint can be obtained. An inverse lifting operation on the generated residual implements its fast rate. The residual evaluation problem is also considered. A numerical example is finally given to illustrate the effectiveness of the proposed design techniques

Fault Detection Filter for Linear Discrete Time-Varying Systems

This note is concerned with the problem of parity space-based fault estimation for linear discrete time-varying systems. The design of parity space-based fault estimator is formulated as to find a minimum for a matrix quadratic form. It is shown that the minimum provides a unified solution to the fault estimation problem with different design criteria, such as the performance indices of maximum singular value and Frobenius-norm. A necessary and sufficient condition for the minimum is derived and an analytic solution to the parity space-based fault estimator is obtained. Numerical examples are given to show the effectiveness of the proposed method.

Observer-Based Fast Rate Fault Detection for a Class of Multirate Sampled-Data Systems

In this paper, a new approach to parity space-based fault detection (FD) is put forward for linear discrete time-varying (LDTV) systems. The focus of our study is on solving the problem with heavy online computational burden. The main contributions are two folds. Firstly, the problem of parity space-based FD is formulated as finding a minimum of quadratic form of unknown input. Secondly, by applying projection in Krein space, a solution of optimal parity space-based FD is obtained via recursively computing innovations. It is shown that the reduction of computation cost is achievable, especially with the increase of parity space order. Finally, a numerical example is given to demonstrate the application of the proposed method.

Parity Space-Based Fault Estimation for Linear Discrete Time-Varying Systems

This paper deals with the fault detection filter design problem for linear time invariant time-delay systems with unknown input. The core of our study is to a) take the behavior of delayed state and measurement into consideration when the observer-based fault detection filter is constructed; b) solve the formulated fault detection filter design problem by combining of using the left eigenstructure assignment approach and H/sub /spl infin// optimization technique. Through a suitable choice of the filter gain matrices and residual weighting matrix, the residual can be completely decoupled from the delay-free unknown input, while the influence of the delayed unknown input on residual is minimized in the sense of H/sub /spl infin// norm. Numerical simulation is used to illustrate the efficiency of the proposed method.

Parity space-based fault detection for linear discrete time-varying systems with unknown input

This article deals with problems of parity space-based fault detection for a class of discrete-time linear Markovian jump systems. A new algorithm is firstly introduced to reduce the computation of mode-dependent redundancy relation parameter matrices. Different from the case of linear time invariant systems, the parity space-based residual generator for a Markovian jump system cannot be designed off-line because it depends on the history of system modes in the last finite steps. In order to overcome this difficulty, a finite set of parity matrices is pre-designed applying a unified approach to linear time invariant systems. Then the on-line residual generation can be easily implemented. Moreover, the problem of residual evaluation is also considered which includes the determination of a residual evaluation function and a threshold. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Fault detection filter design for LTI system with time delays

Abstract This paper deals with the fault detection problem for linear time-invariant systems with unknown disturbances. Two separate performance indices are presented to facilitate the design of desirable fault detection observers. Iterative linear matrix inequality (LMI) algorithms are proposed in order to design a fault detection observer that aims at enhancing the fault detection and attenuating the effects due to unknown inputs. Numerical examples are employed to demonstrate the effectiveness of the proposed methods.

Parity space-based fault detection for Markovian jump systems

This paper is concerned with the design of the fault detection systems, into which a residual generation, evaluation and threshold are integrated, for linear discrete time-varying processes over a finite horizon. In the proposed design scheme, the residual generation is realised in the context of H∞ fault estimation with a prescribed attenuation level. This attenuation level is minimised by using the Krein-space linear estimation theory and, subsequently, an H∞ fault estimator with the minimum attenuation level is designed in terms of the solution to a set of Riccati-like recursions. For the residual evaluation and decision making purpose, the false alarm rate and fault detection rate indicators are introduced in the norm-based framework, which is integrated into the decision making procedure. For the online computations of the false alarm rate and fault detection rate indicators, further estimates delivered by the H∞ fault estimator are applied without additional (online) computations. By means of checking the change in the false alarm rate and fault detection rate indicators, a decision is then made. In this way, the fault detection performance can be significantly improved. Finally, one application example is exploited to demonstrate the application of the proposed integrated fault detection and performance evaluation schemes.