Simultaneous Fault Detection and Control Design for Switched Linear Systems: A Linear Matrix Inequality Approach

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
M. R. Davoodi ◽  
A. Golabi ◽  
H. A. Talebi ◽  
H. R. Momeni
Keyword(s):  
Fault Detection ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Conservative Approach ◽  
Matrix Inequalities ◽  
Linear Matrix Inequality Approach ◽  
And Control ◽  
Selection Of

In this paper, the problem of simultaneous fault detection and control (SFDC) for linear switched systems in discrete- and continuous-time cases under a mixed H−/H∞ framework is considered. In essence, a single unit called detector/controller is designed, where the detector is an observer and the controller is an observer-based controller. The conventional mixed H−/H∞ problem is a conservative approach due to the selection of equal Lyapunov matrices. Extended linear matrix inequalities (LMIs) characterizations are used to reduce the conservativeness by the introduction of additional matrix variables, so as to eliminate the coupling of Lyapunov matrices with the system matrices. Indeed, the idea presented in this paper is based on the average dwell time (ADT) and conservatism reduction approaches, which lead to some sufficient conditions for solving the problem in terms of LMI feasibility conditions. Two examples are provided to demonstrate the effectiveness of the proposed method.

Simultaneous Fault Detection and Control for Continuous-Time Switched T-S Fuzzy Systems with State Jumps

2021 ◽  
Author(s):  
Ayyoub Ait Ladel ◽  
Abdellah Benzaouia ◽  
Rachid Outbib ◽  
Mustapha Ouladsine
Keyword(s):  
Fault Detection ◽  
Fuzzy Systems ◽  
Degrees Of Freedom ◽  
Average Dwell Time ◽  
Single Step ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Robust Detection ◽  
And Control ◽  
Detector Design

Abstract This paper addresses the simultaneous fault detection and control (SFDC) issue for switched T-S fuzzy systems with state jumps. The main objective is to design robust detection filters and observer-based controllers to stabilize this system class and, at the same time, detect the presence of faults. Less conservative stability conditions are developed, applying the mode-dependent average dwell time (MDADT) concept, the robust H_{\infty} approach, and the piecewise Lyapunov function (PLF) technique. Based on these conditions, the integrated controller and detector design is formalized in the form of linear matrix inequalities (LMI) instead of bilinear matrix inequalities (BMI). The proposed LMIs determine the controller/ detector gains simultaneously in a single step, thus offering more degrees of freedom in the design. Finally, a numerical example and two real systems examples are studied to prove the applicability and effectiveness of the obtained results.

Asynchronous H∞ filtering fault detection for discrete-time switched linear systems

2021 ◽  
pp. 014233122110320
Author(s):  
Jinjie Huang ◽  
Xianzhi Hao ◽  
Xiaozhen Pan
Keyword(s):  
Fault Detection ◽  
Linear Systems ◽  
Discrete Time ◽  
Lyapunov Functions ◽  
Evaluation System ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Switched Linear Systems

This article studies the asynchronous H∞ filtering fault detection for discrete-time switched linear systems with mode-dependent average dwell time (MDADT). Firstly, a series of mode-dependent fault detection filters are designed, and augmented with original switched systems to construct a residual evaluation system. However, in practice, the switching of the filter often lags behind the corresponding subsystem. To deal with this, the running time of the subsystem is divided into two parts: the matched and the mismatched. Then the asynchronous switched residual evaluation system is obtained, and global uniform exponential stability (GUES) and exponential H∞ performance of asynchronous switched system are guaranteed by using μ-dependent discontinuous multi-Lyapunov functions and MDADT method. The sufficient conditions for the existence of designed filter are given in terms of linear matrix inequalities (LMIs), and parameter matrices of the designed filter and MDADT can be obtained by solving these LMIs. Finally, the effectiveness of the proposed method is demonstrated by two examples.

scholarly journals H∞/H− Simultaneous fault detection and control for continuous-time linear switched delay systems under asynchronous switching

2018 ◽  
Vol 41 (1) ◽  
pp. 263-275 ◽  
Author(s):  
Hossein Shokouhi-Nejad ◽  
Amir Rikhtehgar Ghiasi ◽  
Mohammad Ali Badamchizadeh ◽  
Saeed Pezeshki
Keyword(s):  
Fault Detection ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Delay Systems ◽  
Linear Matrix ◽  
Asynchronous Switching ◽  
State Delay ◽  
Performance Indexes ◽  
And Control

In this paper, the problem of simultaneous fault detection and control for continuous-time switched state-delay systems under asynchronous switching is investigated. The aim is to design a detector/controller unit where the detector is an observer and the controller is an observer-based controller. Based on the average dwell time approach, a new method is proposed where both stability and fault detection are considered, simultaneously, through certain performance indexes. This problem is formulated as a mixed H∞/ H− problem and its solution leads to new sufficient conditions in the form of linear matrix inequality feasibility conditions. The effectiveness of the design technique is illustrated via an example.

Exponential stability and periodicity of memristor-based recurrent neural networks with time-varying delays

2017 ◽  
Vol 10 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Wei Zhang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Inclusion Theory ◽  
The Stability

In this paper, the stability and periodicity of memristor-based neural networks with time-varying delays are studied. Based on linear matrix inequalities, differential inclusion theory and by constructing proper Lyapunov functional approach and using linear matrix inequality, some sufficient conditions are obtained for the global exponential stability and periodic solutions of memristor-based neural networks. Finally, two illustrative examples are given to demonstrate the results.

scholarly journals Robust Observer Design for Switched Positive Linear System with Uncertainties

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yanke Zhong ◽  
Tefang Chen
Keyword(s):  
Linear System ◽  
Linear Matrix Inequality ◽  
Dwell Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Observer Design ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Robust Observer ◽  
Slack Variable

This paper is concerned with the design of a robust observer for the switched positive linear system with uncertainties. Sufficient conditions of building a robust observer are established by using the multiple copositive Lyapunov-krasovskii function and the average dwell time approach. By introducing an auxiliary slack variable, these sufficient conditions are transformed into LMI (linear matrix inequality). A numerical example is given to illustrate the validities of obtained results.

The Application of Linear Algebra Algorithm in the Production of Linear Matrix Inequalities

2012 ◽  
Vol 192 ◽  
pp. 406-411
Author(s):  
Hui Zhang
Keyword(s):  
Problem Solving ◽  
Linear Algebra ◽  
Linear Matrix Inequalities ◽  
Polynomial Matrix ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Application System ◽  
And Control ◽  
Problem Data

Discusses the theory and symbolic of the algorithm gives another potential application, but also in the system and control. For example, for the question, has made with special structure, but LMI problem data, may cause factorizations LMI more compact. One can even imagine using the algorithm around, looking for the opportunity to LMI automatic eliminate variables, so simplify problem solving, before they get a lot of influence and a potential solutions. We describe theory, the algorithm can be used to factor in the non commuting variable polynomial matrix and application system switches and control problem into a linear matrix inequality.

STABILITY ANALYSIS FOR DELAYED CELLULAR NEURAL NETWORKS BASED ON LINEAR MATRIX INEQUALITY APPROACH

2004 ◽  
Vol 14 (09) ◽  
pp. 3377-3384 ◽  
Author(s):  
XIAOFENG LIAO ◽  
KWOK-WO WONG ◽  
SHIZHONG YANG
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Linear Matrix Inequality Approach ◽  
Functional Differential ◽  
The Stability

Some sufficient conditions for the asymptotic stability of cellular neural networks with time delay are derived using the Lyapunov–Krasovskii stability theory for functional differential equations as well as the linear matrix inequality (LMI) approach. The analysis shows how some well-known results can be refined and generalized in a straightforward manner. Moreover, the stability criteria obtained are delay-independent. They are less conservative and restrictive than those reported so far in the literature, and provide a more general set of criteria for determining the stability of delayed cellular neural networks.

Robust Unknown Input Observer for Nonlinear Systems and Its Application to Fault Detection and Isolation

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
S. Mondal ◽  
G. Chakraborty ◽  
K. Bhattacharyya
Keyword(s):  
Fault Diagnosis ◽  
Nonlinear System ◽  
Fault Detection ◽  
Nonlinear Function ◽  
Fault Detection And Isolation ◽  
Linear Matrix ◽  
Unknown Input ◽  
Matrix Inequality ◽  
Unknown Input Observer ◽  
Linear Matrix Inequality Approach

A robust unknown input observer for a nonlinear system whose nonlinear function satisfies the Lipschitz condition is designed based on linear matrix inequality approach. Both noise and uncertainties are taken into account in deriving the observer. A component fault detection and isolation scheme based on these observers is proposed. The effectiveness of the observer and the fault diagnosis scheme is shown by applying them for component fault diagnosis of an electrohydraulic actuator.

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