Fault detection for switched systems with finite-frequency specifications

This paper is concerned with the fault detection filter design problem for a class of discrete-time switched systems whose output can track a time-varying and known frequency region reference input under arbitrary switchings. Faults detection filters are designed to guarantee that the disturbance attenuation performance is satisfied for all subsystems, the reference input attenuation performance is satisfied for the fault-free case, meanwhile, the reference input sensitivity performance is satisfied for the fault cases. With the aid of virtue of the frequency of the reference input in the finite-frequency region which is known beforehand, the finite-frequency H− performance for switched systems is firstly defined. Sufficient conditions for the fault detection filter are given in terms of solutions to a set of linear matrix inequalities, furthermore, the filter gains are characterized in terms of the solution of a convex optimization problem. A numerical example is used to demonstrate the effectiveness of the proposed design method.

[1]  Jun Zhao,et al.  Stabilization of switched nonlinear systems with passive and non-passive subsystems , 2012 .

[2]  Karolos M. Grigoriadis,et al.  Robust fault estimation of uncertain systems using an LMI‐based approach , 2008 .

[3]  Yonggang Chen,et al.  Stabilization of impulsive switched linear systems with saturated control input , 2012 .

[4]  A. Morse,et al.  Basic problems in stability and design of switched systems , 1999 .

[5]  Ho Jae Lee,et al.  sensor fault detection observer design for nonlinear systems in Takagi–Sugeno’s form , 2012 .

[6]  Bo Hu,et al.  Disturbance attenuation properties of time-controlled switched systems , 2001, J. Frankl. Inst..

[7]  Jonathan P. How,et al.  Modeling and H∞ control for switched linear parameter-varying missile autopilot , 2003, IEEE Trans. Control. Syst. Technol..

[8]  Bin Jiang,et al.  Fault detection for discrete-time switched systems with interval time-varying delays , 2011 .

[9]  Inseok Hwang,et al.  A Survey of Fault Detection, Isolation, and Reconfiguration Methods , 2010, IEEE Transactions on Control Systems Technology.

[10]  Hai Lin,et al.  Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results , 2009, IEEE Transactions on Automatic Control.

[11]  Xinzhi Liu,et al.  Reduced-order fault detection filter design for switched nonlinear systems with time delay , 2012 .

[12]  Torsten Jeinsch,et al.  A unified approach to the optimization of fault detection systems , 2000 .

[13]  Peng Shi,et al.  Robust Fault Detection for Switched Linear Systems With State Delays , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[14]  M. Branicky.  Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[15]  Fen Wu,et al.  Switching LPV control of an F-16 aircraft via controller state reset , 2006, IEEE Trans. Control. Syst. Technol..

[16]  Georgi M. Dimirovski,et al.  Output feedback control for uncertain linear systems with faulty actuators based on a switching method , 2009 .

[17]  Guang-Hong Yang,et al.  Finite frequency H∞ filtering for uncertain discrete-time switched linear systems , 2009 .

[18]  Fred Y. Hadaegh,et al.  Stability Analysis of Switched Dynamical Systems with State-Space Dilation and Contraction , 2006 .

[19]  Jie Lian,et al.  Sliding-mode control of switched delay systems with nonlinear perturbations: average dwell time approach , 2010 .

[20]  Peng Shi,et al.  Fault detection for discrete-time switched systems with intermittent measurements , 2012, Int. J. Control.

[21]  Imad M. Jaimoukha,et al.  A matrix factorization solution to the I fault detection problem , 2006, Autom..

[22]  Jamal Daafouz,et al.  Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach , 2002, IEEE Trans. Autom. Control..

[23]  Heng Wang,et al.  Fault Detection for a Class of Uncertain State-Feedback Control Systems , 2010, IEEE Transactions on Control Systems Technology.

[24]  Huijun Gao,et al.  Robust H∞ filtering for switched linear discrete‐time systems with polytopic uncertainties , 2006 .

[25]  Heng Wang,et al.  A finite frequency domain approach to fault detection for linear discrete-time systems , 2008, Int. J. Control.