An improved H∞ filter design for nonlinear systems described by T-S fuzzy models with time-varying delay

This paper addresses a robust H∞ filter design problem for nonlinear systems with time-varying delay through Takagi-Sugeno (T-S) fuzzy model approach. Firstly, by introducing free-weighting matrix method combined with a matrix decoupling approach and adopting an improved integral inequality method without ignoring any integral term, less conservative results are achieved. Next, based on the model, new delay-dependent sufficient conditions are derived, which are less conservative than the existing ones via solving the linear matrix inequalities (LMIs). Lastly, simulations show a significant improvement over the previous results.

[1]  Yuanqing Xia,et al.  New Results on H∞ Filtering for Fuzzy Time-Delay Systems , 2009, IEEE Trans. Fuzzy Syst..

[2]  M. Mahmoud.  Resilient L/sub 2/-L∞ filtering of polytopic systems with state delays , 2007 .

[3]  Pedro Luis Dias Peres,et al.  Robust H∞ filter design for uncertain linear systems with multiple time-varying state delays , 2001, IEEE Trans. Signal Process..

[4]  Qing-Long Han,et al.  A New $H_{{\bm \infty}}$ Stabilization Criterion for Networked Control Systems , 2008, IEEE Transactions on Automatic Control.

[5]  Tong Heng Lee,et al.  $H_{\infty} $ Filter Design for Nonlinear Systems With Time-Delay Through T–S Fuzzy Model Approach , 2008, IEEE Transactions on Fuzzy Systems.

[6]  Lihua Xie,et al.  H∞ estimation for discrete-time linear uncertain systems , 1991 .

[7]  Huijun Gao,et al.  A delay-dependent approach to robust H∞ filtering for uncertain discrete-time state-delayed systems , 2004, IEEE Trans. Signal Process..

[8]  Qing-Long Han,et al.  Sampled-data H∞ filtering of Takagi-Sugeno fuzzy systems with interval time-varying delays , 2014, J. Frankl. Inst..

[9]  M. Grimble,et al.  A New Approach to the H ∞ Design of Optimal Digital Linear Filters , 1989 .

[10]  Qing-Long Han,et al.  On Designing Fuzzy Controllers for a Class of Nonlinear Networked Control Systems , 2008, IEEE Transactions on Fuzzy Systems.

[11]  H. Unbehauen,et al.  Robust H∞ observer design of linear time-delay systems with parametric uncertainty , 2001 .

[12]  Qing-Long Han,et al.  Robust Hinfinity filtering for a class of uncertain linear systems with time-varying delay , 2008, Autom..

[13]  Keith J. Burnham,et al.  On designing observers for time-delay systems with non-linear disturbances , 2002 .

[14]  Dong Yue,et al.  Network-based robust H ∞ control of systemswith uncertainty , 2005 .

[15]  Yuanqing Xia,et al.  Design and Stability Criteria of Networked Predictive Control Systems With Random Network Delay in the Feedback Channel , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[16]  Guang-Hong Yang,et al.  Fault Tolerant Controller Design for T–S Fuzzy Systems With Time-Varying Delay and Actuator Faults: A K-Step Fault-Estimation Approach , 2014, IEEE Transactions on Fuzzy Systems.

[17]  Qing-Long Han,et al.  New stability criteria for linear systems with interval time-varying delay , 2008, Autom..

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

[19]  Jinliang Liu,et al.  H 8 Filtering for time‐delay systems with Markovian jumping parameters: Delay partitioning approach , 2010 .

[20]  Huaguang Zhang,et al.  A new fuzzy H∞ filter design for nonlinear continuous-time dynamic systems with time-varying delays , 2009, Fuzzy Sets Syst..

[21]  Q. Han,et al.  Novel delay‐derivative‐dependent stability criteria using new bounding techniques , 2013 .

[22]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[23]  Junmin Li,et al.  Adaptive iterative learning control for nonlinear time-delay systems with periodic disturbances using FSE-neural network , 2011, Int. J. Autom. Comput..

[24]  J. Lam,et al.  A delay-dependent approach to robust H/sub /spl infin// filtering for uncertain distributed delay systems , 2005, IEEE Transactions on Signal Processing.

[25]  Xi-Qin He,et al.  New Results on $H_\infty$ Filter Design for Nonlinear Systems With Time Delay via T–S Fuzzy Models , 2011, IEEE Transactions on Fuzzy Systems.

[26]  Jian Sun,et al.  Delay-Dependent Robust H∞ Filter Design for Uncertain Linear Systems with Time-Varying Delay , 2009, Circuits Syst. Signal Process..

[27]  Dan Zhang,et al.  $H_\infty$ Filtering for Networked Systems With Multiple Time-Varying Transmissions and Random Packet Dropouts , 2013, IEEE Transactions on Industrial Informatics.

[28]  James Lam,et al.  New approach to mixed H/sub 2//H/sub /spl infin// filtering for polytopic discrete-time systems , 2005, IEEE Transactions on Signal Processing.

[29]  Uri Shaked,et al.  𝒽∞ Filtering for Continuous-time Linear Systems with Delay , 1999, IEEE Trans. Autom. Control..

[30]  Xiefu Jiang,et al.  Delay-dependent H/sub /spl infin// filter design for linear systems with interval time-varying delay , 2007 .

[31]  Shengyuan Xu,et al.  An LMI approach to the H∞ filter design for uncertain systems with distributed delays , 2004, IEEE Trans. Circuits Syst. II Express Briefs.

[32]  Q. Han,et al.  New stability criterion using a matrix-based quadratic convex approach and some novel integral inequalities , 2014 .

[33]  Pan Wang,et al.  Adaptive H∞ Control for Nonlinear Hamiltonian Systems with Time Delay and Parametric Uncertainties , 2014, Int. J. Autom. Comput..

[34]  E. Sánchez,et al.  OPTIMAL LINEAR FILTERING FOR SYSTEMS WITH MULTIPLE STATE AND OBSERVATION DELAYS , 2007 .