ℋ−/ℋ∞ memory fault detection filtering design for uncertain systems with finite frequency specifications

This article is concerned with the ℋ−/ℋ∞ memory fault detection filtering design in finite frequency domain for discrete‐time systems with polytopic uncertainties. Under the assumption that both disturbances and faults are restricted to finite frequency ranges, that is, the low, middle, or high frequency range, an admissible memory fault detection filter is developed by using historical information of the system. It is shown that the asymptotic stability with prescribed ℋ−/ℋ∞ performance of the closed‐loop filtering error system is guaranteed. It is also shown that by using historical system outputs along with parameter‐dependent Lyapunov functions, the better performance of the resulting fault detection filter is obtained. With the aid of Projection lemma, sufficient conditions for the fault detection filtering design are established by solving an optimization problem in the form of a set of linear matrix inequalities (LMIs). Finally, three examples are presented to demonstrate the effectiveness and advantages of the proposed approach.

[1]  R. J. Patton,et al.  An LMI approach to H - /H∞ fault detection observers , 2002 .

[2]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in System and Control Theory , 1994, Studies in Applied Mathematics.

[3]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[4]  Jie Chen,et al.  Robust Model-Based Fault Diagnosis for Dynamic Systems , 1998, The International Series on Asian Studies in Computer and Information Science.

[5]  Dominique Sauter,et al.  Optimal thresholding for robust fault detection of uncertain systems , 2000 .

[6]  Marios M. Polycarpou,et al.  A robust detection and isolation scheme for abrupt and incipient faults in nonlinear systems , 2002, IEEE Trans. Autom. Control..

[7]  S. Nguang,et al.  H/sub /spl infin// filtering for fuzzy dynamical systems with D stability constraints , 2003 .

[8]  Shinji Hara,et al.  Generalized KYP lemma: unified frequency domain inequalities with design applications , 2005, IEEE Transactions on Automatic Control.

[9]  Shinji Hara,et al.  Time domain interpretations of frequency domain inequalities on (semi)finite ranges , 2005, Syst. Control. Lett..

[10]  Jian Liu,et al.  An LMI approach to minimum sensitivity analysis with application to fault detection , 2005, Autom..

[11]  Lihua Xie,et al.  A generalized KYP lemma based approach for disturbance rejection in data storage systems , 2007, Autom..

[12]  Guang-Hong Yang,et al.  A finite frequency approach to filter design for uncertain discrete‐time systems , 2008 .

[13]  Steven X. Ding,et al.  Model-based Fault Diagnosis Techniques: Design Schemes, Algorithms, and Tools , 2008 .

[14]  Edoardo Mosca,et al.  A robust fault detection and isolation filter design under sensitivity constraint: An LMI approach , 2008 .

[15]  Yu Cui,et al.  Design and analysis of robust fault detection filter using LMI tools , 2009, Comput. Math. Appl..

[16]  Heng Wang,et al.  Integrated fault detection and control for LPV systems , 2009 .

[17]  Yang Chen,et al.  Finite frequency H∞ control for building under earthquake excitation , 2010 .

[18]  Guang-Hong Yang,et al.  Fuzzy Filter Design for Nonlinear Systems in Finite-Frequency Domain , 2010, IEEE Transactions on Fuzzy Systems.

[19]  I. Jaimoukha,et al.  State–space solution to the ℋ︁−/ℋ︁∞ fault‐detection problem , 2012 .

[20]  Steven X. Ding,et al.  H_/H∞ fault detection filter design for discrete-time Takagi-Sugeno fuzzy system , 2013, Autom..

[21]  Guang-Hong Yang,et al.  Fault detection and isolation for networked control systems with finite frequency specifications , 2014 .

[22]  Huijun Gao,et al.  Robust Filtering for Uncertain Systems: A Parameter-Dependent Approach , 2014 .

[23]  Guang-Hong Yang,et al.  Fault Detection in Finite Frequency Domain for Takagi-Sugeno Fuzzy Systems With Sensor Faults , 2014, IEEE Transactions on Cybernetics.

[24]  Young Hoon Joo,et al.  Periodically Time-Varying ${\cal H}_{\infty}$ Memory Filter Design for Discrete-Time LTI Systems With Polytopic Uncertainty , 2014, IEEE Transactions on Automatic Control.

[25]  Steven X. Ding,et al.  A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches , 2015, IEEE Transactions on Industrial Electronics.

[26]  Denis Efimov,et al.  H ∞  ∕ H −  LPV solutions for fault detection of aircraft actuator faults: Bridging the gap between theory and practice , 2015 .

[27]  Guang-Hong Yang,et al.  Fault Detection for Discrete-Time Switched Systems in Finite-Frequency Domain , 2015, Circuits Syst. Signal Process..

[28]  H. Karimi,et al.  Discrete‐time H −  ∕ H ∞  sensor fault detection observer design for nonlinear systems with parameter uncertainty , 2015 .

[29]  Tasawar Hayat,et al.  On Design of Robust Fault Detection Filter in Finite-Frequency Domain With Regional Pole Assignment , 2015, IEEE Transactions on Circuits and Systems II: Express Briefs.

[30]  Guang-Hong Yang,et al.  Fault detection filter design for stochastic networked control systems , 2015 .

[31]  Guang-Hong Yang,et al.  Fault detection filter design with adaptive mechanism for linear uncertain polytopic systems in finite frequency domains , 2016 .

[32]  Ricardo C. L. F. Oliveira,et al.  Robust H∞ filter design with past output measurements for uncertain discrete-time systems , 2016, Autom..

[33]  Peng Shi,et al.  H- / H∞ fault detection observer in finite frequency domain for linear parameter-varying descriptor systems , 2017, Autom..

[34]  Kezhen Han,et al.  Memory scheduling robust H ∞ filter-based fault detection for discrete-time polytopic uncertain systems over fading channels , 2017 .

[35]  Jian Feng,et al.  Robust periodically time‐varying horizon finite memory fault detection filter design for polytopic uncertain discrete‐time systems , 2017 .

[36]  Jun Hu,et al.  Joint state and fault estimation for time-varying nonlinear systems with randomly occurring faults and sensor saturations , 2018, Autom..

[37]  Hamid Reza Karimi,et al.  A Novel Memory Filtering Design for Semi-Markovian Jump Time-Delay Systems , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[38]  Steven X. Ding,et al.  Design of robust fuzzy fault detection filter for polynomial fuzzy systems with new finite frequency specifications , 2018, Autom..

[39]  Meng Wang,et al.  Finite Frequency Filtering Design for Uncertain Discrete-Time Systems Using Past Output Measurements , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

[40]  Hamid Reza Karimi,et al.  Fuzzy-Affine-Model-Based Memory Filter Design of Nonlinear Systems With Time-Varying Delay , 2018, IEEE Transactions on Fuzzy Systems.

[41]  Weixin Han,et al.  H−/L∞ fault detection observer for linear parameter‐varying systems with parametric uncertainty , 2019 .

[42]  Fuad E. Alsaadi,et al.  Detection of intermittent faults for nonuniformly sampled multi-rate systems with dynamic quantisation and missing measurements , 2018, Int. J. Control.

[43]  Meng Wang,et al.  A Novel Piecewise Affine Filtering Design for T–S Fuzzy Affine Systems Using Past Output Measurements , 2020, IEEE Transactions on Cybernetics.

[44]  Jianbin Qiu,et al.  Membership-Function-Dependent Fault Detection Filtering Design for Interval Type-2 T–S Fuzzy Systems in Finite Frequency Domain , 2021, IEEE Transactions on Fuzzy Systems.

[45]  Hao Zhang,et al.  Fault Detection Filtering Design for Discrete-Time Interval Type-2 T–S Fuzzy Systems in Finite Frequency Domain , 2021, IEEE Transactions on Fuzzy Systems.