On the robust design of unknown inputs Takagi-Sugeno observer

This paper deals with the observer design for Takagi-Sugeno (T-S) fuzzy models subject to unknown inputs and disturbance affecting both states and outputs of the system. Sufficient conditions to design an unknown input T-S observer are given in Linear Matrix Inequalities (LMIs) terms. Relaxations are introduced by using intermediate variables. Numerical example is given to illustrate the effectiveness of the given result.

[1]  Kazuo Tanaka,et al.  A Descriptor System Approach to Fuzzy Control System Design via Fuzzy Lyapunov Functions , 2007, IEEE Transactions on Fuzzy Systems.

[2]  J. Bernussou,et al.  A new robust D-stability condition for real convex polytopic uncertainty , 2000 .

[3]  T. Floquet,et al.  A sliding mode approach of unknown input observers for linear systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[4]  Michel Kinnaert,et al.  Diagnosis and Fault-Tolerant Control , 2004, IEEE Transactions on Automatic Control.

[5]  James Lam,et al.  Stability Analysis and Stabilization for Discrete-Time Fuzzy Systems With Time-Varying Delay , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[6]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[7]  Peng Shi,et al.  Integrated Fault Estimation and Accommodation Design for Discrete-Time Takagi–Sugeno Fuzzy Systems With Actuator Faults , 2011, IEEE Transactions on Fuzzy Systems.

[8]  Antonio Sala,et al.  Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Polya's theorem , 2007, Fuzzy Sets Syst..

[9]  Nurkan Yagiz,et al.  Robust control of a spatial robot using fuzzy sliding modes , 2009, Math. Comput. Model..

[10]  Huijun Gao,et al.  H∞ Fuzzy Control of Nonlinear Systems Under Unreliable Communication Links , 2009, IEEE Trans. Fuzzy Syst..

[11]  P. Shi,et al.  Robust H∞ Output Feedback Control Design for Takagi-Sugeno Systems with Markovian Jumps: A Linear Matrix Inequality Approach , 2006 .

[12]  R. W. Wilde,et al.  Observers for linear systems with unknown inputs , 1988 .

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

[14]  Sheng-Fuu Lin,et al.  Unknown input observers for singular systems designed by eigenstructure assignment , 2003, J. Frankl. Inst..

[15]  Vassilis L. Syrmos,et al.  Computational Observer Design Techniques in Linear Systems with Unknown Inputs using the Concept of Transmission Zeros , 1992 .

[16]  Ahmed El Hajjaji,et al.  Robust observer-based fault-tolerant control for vehicle lateral dynamics , 2008 .

[17]  Hieu Minh Trinh,et al.  State and input simultaneous estimation for a class of nonlinear systems , 2004, Autom..

[18]  Damien Koenig,et al.  Unknown input proportional multiple-integral observer design for linear descriptor systems: application to state and fault estimation , 2005, IEEE Transactions on Automatic Control.

[19]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[20]  Thierry-Marie Guerra,et al.  Nonquadratic Stabilization Conditions for a Class of Uncertain Nonlinear Discrete Time TS Fuzzy Models: A New Approach , 2008, IEEE Transactions on Automatic Control.

[21]  Ron J. Patton,et al.  FAULT-TOLERANT CONTROL SYSTEMS: THE 1997 SITUATION , 1997 .

[22]  Stephen P. Boyd,et al.  Semidefinite Programming , 1996, SIAM Rev..

[23]  K. S. Banerjee Generalized Inverse of Matrices and Its Applications , 1973 .

[24]  Kazuo Tanaka,et al.  A multiple Lyapunov function approach to stabilization of fuzzy control systems , 2003, IEEE Trans. Fuzzy Syst..

[25]  Roderick Murray-Smith,et al.  Multiple Model Approaches to Modelling and Control , 1997 .

[26]  James Lam,et al.  Stability and Stabilization of Delayed T--S Fuzzy Systems: A Delay Partitioning Approach , 2009, IEEE Transactions on Fuzzy Systems.

[27]  S. A. Bøgh Fault Tolerant Control Systems , 1997 .

[28]  E. A. Woods,et al.  Fault detection, supervision and safety for technical processes , 1993 .

[29]  Guo-Ping Jiang,et al.  Design of observer with integrators for linear systems with unknown input disturbances , 2000 .

[30]  Pierre Apkarian,et al.  Continuous-time analysis, eigenstructure assignment, and H2 synthesis with enhanced linear matrix inequalities (LMI) characterizations , 2001, IEEE Trans. Autom. Control..

[31]  C. R. Rao,et al.  Generalized Inverse of Matrices and its Applications , 1972 .

[32]  Mohammed Chadli,et al.  An LMI approach to design observer for unknown inputs Takagi‐Sugeno fuzzy models , 2010 .

[33]  L. Xiaodong,et al.  New approaches to H∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI , 2003, Autom..

[34]  M. Saif,et al.  A novel approach to the design of unknown input observers , 1991 .

[35]  James Lam,et al.  $H_{\bm \infty}$ Fuzzy Filtering of Nonlinear Systems With Intermittent Measurements , 2009, IEEE Transactions on Fuzzy Systems.