Relaxed filtering designs for continuous-time nonlinear systems via novel fuzzy H∞ filters

This paper investigates the problem of H ∞ filtering for continuous-time nonlinear systems in the Takagi-Sugeno (T-S) fuzzy model form. Different from the existing fuzzy H ∞ filters, a novel filter is designed such that the filter matrices are homogeneous polynomially parameter dependent on membership functions with an arbitrary degree. By developing both the novel fuzzy H ∞ filter and a kind of slack matrix variable technique, relaxed filtering conditions for implementing the H ∞ filter are proposed in terms of linear matrix inequalities (LMIs), while the filtering error system preserves a smaller prescribed H ∞ performance index than the existing ones. Finally, a numerical example is given to illustrate to show the effectiveness of the proposed approach. Highlights? A new fuzzy H ∞ filter is developed for continuous-time nonlinear systems. ? The criterion takes the form of an LMI and is computationally tractable. ? The filtering conditions turn out to be less conservative than previously reported criteria.

[1]  Jianbin Qiu,et al.  A New Design of Delay-Dependent Robust ${\cal H}_{\bm \infty}$ Filtering for Discrete-Time T--S Fuzzy Systems With Time-Varying Delay , 2009, IEEE Transactions on Fuzzy Systems.

[2]  Xin-Ping Guan,et al.  H∞ filtering of time-delay T-S fuzzy systems based on piecewise Lyapunov-Krasovskii functional , 2009, Signal Process..

[3]  Jianbin Qiu,et al.  A new design of delay‐dependent robust ℋ︁∞ filtering for continuous‐time polytopic systems with time‐varying delay , 2010, International Journal of Robust and Nonlinear Control.

[4]  Yongduan Song,et al.  A Novel Approach to Filter Design for T–S Fuzzy Discrete-Time Systems With Time-Varying Delay , 2012, IEEE Transactions on Fuzzy Systems.

[5]  Ligang Wu,et al.  A New Approach to Stability Analysis and Stabilization of Discrete-Time T-S Fuzzy Time-Varying Delay Systems , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[6]  Jianbin Qiu,et al.  Model Approximation for Discrete-Time State-Delay Systems in the T–S Fuzzy Framework , 2011, IEEE Transactions on Fuzzy Systems.

[7]  Xiangpeng Xie,et al.  Relaxed Stability Conditions for Continuous-Time T–S Fuzzy-Control Systems Via Augmented Multi-Indexed Matrix Approach , 2011, IEEE Transactions on Fuzzy Systems.

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

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

[10]  Guang-Hong Yang,et al.  Relaxed stabilization conditions for continuous-time Takagi-Sugeno fuzzy control systems , 2010, Inf. Sci..

[11]  TanakaK.,et al.  An approach to fuzzy control of nonlinear systems , 1996 .

[12]  Bernardino Castillo-Toledo,et al.  Exact Output Regulation for Nonlinear Systems Described by Takagi–Sugeno Fuzzy Models , 2012, IEEE Transactions on Fuzzy Systems.

[13]  Huaguang Zhang,et al.  Fuzzy $H_\infty$ Filter Design for a Class of Nonlinear Discrete-Time Systems With Multiple Time Delays , 2007, IEEE Transactions on Fuzzy Systems.

[14]  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.

[15]  Jinliang Liu,et al.  H∞ filter design for nonlinear systems with time-delay through T-S fuzzy model approach , 2010, 2010 Chinese Control and Decision Conference.

[16]  Ligang Wu,et al.  Fuzzy filtering of nonlinear fuzzy stochastic systems with time-varying delay , 2009, Signal Process..

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

[18]  Jianbin Qiu,et al.  Fuzzy-Model-Based Piecewise ${\mathscr H}_{\infty }$ Static-Output-Feedback Controller Design for Networked Nonlinear Systems , 2010, IEEE Transactions on Fuzzy Systems.

[19]  Robert E. Skelton,et al.  Stability tests for constrained linear systems , 2001 .

[20]  Daniel W. C. Ho,et al.  Fuzzy Filter Design for ItÔ Stochastic Systems With Application to Sensor Fault Detection , 2009, IEEE Transactions on Fuzzy Systems.

[21]  Shengyuan Xu,et al.  Fuzzy weighting-dependent approach to robust L , 2009, Signal Process..

[22]  Jianbin Qiu,et al.  Nonsynchronized-State Estimation of Multichannel Networked Nonlinear Systems With Multiple Packet Dropouts Via T–S Fuzzy-Affine Dynamic Models , 2011, IEEE Transactions on Fuzzy Systems.

[23]  Xiao‐Heng Chang.  A Descriptor Representation Approach , 2012 .

[24]  Daniel W. C. Ho,et al.  Robust ${{\cal H}}_{\infty}$ Filtering for Markovian Jump Systems With Randomly Occurring Nonlinearities and Sensor Saturation: The Finite-Horizon Case , 2011, IEEE Transactions on Signal Processing.

[25]  Huijun Gao,et al.  A Parameter-Dependent Approach to Robust $H_{\infty }$ Filtering for Time-Delay Systems , 2008, IEEE Transactions on Automatic Control.

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

[27]  Huijun Gao,et al.  A new design of robust H2 filters for uncertain systems , 2008, Syst. Control. Lett..

[28]  Huijun Gao,et al.  Title H ∞ fuzzy filtering of nonlinear systems with intermittentmeasurements , 2009 .

[29]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[30]  Daniel W. C. Ho,et al.  Variance-Constrained ${\cal H}_{\infty}$ Filtering for a Class of Nonlinear Time-Varying Systems With Multiple Missing Measurements: The Finite-Horizon Case , 2010, IEEE Transactions on Signal Processing.

[31]  Yang Shi,et al.  Improved robust energy-to-peak filtering for uncertain linear systems , 2010, Signal Process..

[32]  James Lam,et al.  Fuzzy-Model-Based Robust Fault Detection With Stochastic Mixed Time Delays and Successive Packet Dropouts , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[33]  Ricardo C. L. F. Oliveira,et al.  Parameter-dependent H2 and Hinfinity filter design for linear systems with arbitrarily time-varying parameters in polytopic domains , 2008, Signal Process..

[34]  Huijun Gao,et al.  New results on H∞ filtering for fuzzy systems with interval time-varying delays , 2011, Inf. Sci..

[35]  Ricardo C. L. F. Oliveira,et al.  Hinfinity filtering for discrete-time linear systems with bounded time-varying parameters , 2010, Signal Process..

[36]  Kazuo Tanaka,et al.  An approach to fuzzy control of nonlinear systems: stability and design issues , 1996, IEEE Trans. Fuzzy Syst..

[37]  Guang-Hong Yang,et al.  Non-fragile Hinfinity filter design for linear continuous-time systems , 2008, Autom..

[38]  Guang-Hong Yang,et al.  Non-fragile fuzzy H∞ filter design for nonlinear continuous-time systems with D stability constraints , 2012, Signal Process..

[39]  M. MendelJ.,et al.  Fuzzy basis functions , 1995 .

[40]  Yingmin Jia,et al.  H-infinity filtering for a class of nonlinear discrete-time systems based on unscented transform , 2010, Signal Process..

[41]  Zidong Wang,et al.  Variance-Constrained Filtering for a Class of Nonlinear Time-Varying Systems With Multiple Missing Measurements : The Finite-Horizon Case , 2010 .

[42]  Guang-Hong Yang,et al.  Nonfragile $H_{\infty}$ Filtering of Continuous-Time Fuzzy Systems , 2011, IEEE Transactions on Signal Processing.

[43]  L X Wang,et al.  Fuzzy basis functions, universal approximation, and orthogonal least-squares learning , 1992, IEEE Trans. Neural Networks.

[44]  Huijun Gao,et al.  Robust $H_{\infty}$ Filtering for a Class of Nonlinear Networked Systems With Multiple Stochastic Communication Delays and Packet Dropouts , 2010, IEEE Transactions on Signal Processing.

[45]  Xiangpeng Xie,et al.  Control Synthesis of Discrete-Time T–S Fuzzy Systems Based on a Novel Non-PDC Control Scheme , 2013, IEEE Transactions on Fuzzy Systems.

[46]  Huijun Gao,et al.  I filtering for 2D Markovian jump systems , 2008, Autom..