Observer design of discrete-time T-S fuzzy systems via multi-instant augmented multi-indexed matrix approach

Abstract The problem of relaxed observer design for discrete-time Takagi–Sugeno (T–S) fuzzy systems is addressed in this paper. With the framework of improved homogenous matrix polynomials, a novel kind of slack variable approach, which is homogenous polynomially parameter-dependent on multi-instant normalized fuzzy weighting functions with arbitrary degrees, is proposed by developing an efficient multi-instant augmented multi-indexed matrix approach. Since the algebraic properties of multi-instant normalized fuzzy weighting functions are collected into a set of augmented multi-indexed matrices, more information about multi-instant normalized fuzzy weighting functions can be involved into observer design. As a result, the relaxation quality of fuzzy observer design can be significantly improved. Finally, two numerical examples are given to illustrate the effectiveness of the proposed results.

[1]  Baocang Ding,et al.  Stabilization of Takagi–Sugeno Model via Nonparallel Distributed Compensation Law , 2008, IEEE Transactions on Fuzzy Systems.

[2]  Thierry-Marie Guerra,et al.  Control Law Proposition for the Stabilization of Discrete Takagi–Sugeno Models , 2009, IEEE Transactions on Fuzzy Systems.

[3]  Ricardo C. L. F. Oliveira,et al.  Selective $\hbox{\scr H}_2$ and $\hbox{\scr H}_\infty$ Stabilization of Takagi–Sugeno Fuzzy Systems , 2011, IEEE Transactions on Fuzzy Systems.

[4]  LeeDong Hwan,et al.  Improvement on nonquadratic stabilization of discrete-time Takagi-Sugeno fuzzy systems , 2010 .

[5]  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.

[6]  Jin Bae Park,et al.  Improvement on Nonquadratic Stabilization of Discrete-Time Takagi–Sugeno Fuzzy Systems: Multiple-Parameterization Approach , 2010, IEEE Transactions on Fuzzy Systems.

[7]  Shumin Fei,et al.  Nonquadratic Stabilization of Continuous T–S Fuzzy Models: LMI Solution for a Local Approach , 2012, IEEE Transactions on Fuzzy Systems.

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

[9]  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.

[10]  Hamid Reza Karimi,et al.  Observer-based finite-time fuzzy H∞ control for discrete-time systems with stochastic jumps and time-delays , 2014, Signal Process..

[11]  Peng Shi,et al.  Stochastic finite-time state estimation for discrete time-delay neural networks with Markovian jumps , 2015, Neurocomputing.

[12]  Xian Zhang,et al.  Fuzzy-Model-Based ${{\cal D}}$-Stability and Nonfragile Control for Discrete-Time Descriptor Systems With Multiple Delays , 2014, IEEE Transactions on Fuzzy Systems.

[13]  J. Lauber,et al.  An Efficient Lyapunov Function for Discrete T–S Models: Observer Design , 2012, IEEE Transactions on Fuzzy Systems.

[14]  Hamid Reza Karimi,et al.  Robust Observer Design for Unknown Inputs Takagi–Sugeno Models , 2013, IEEE Transactions on Fuzzy Systems.

[15]  Guang-Hong Yang,et al.  A descriptor representation approach to observer-based Hinfinity control synthesis for discrete-time fuzzy systems , 2011, Fuzzy Sets Syst..

[16]  Ligang Wu,et al.  State estimation and sliding mode control for semi-Markovian jump systems with mismatched uncertainties , 2015, Autom..

[17]  Xiangpeng Xie,et al.  Observer Design of Discrete-Time T–S Fuzzy Systems Via Multi-Instant Homogenous Matrix Polynomials , 2014, IEEE Transactions on Fuzzy Systems.

[18]  Huaguang Zhang,et al.  Stability Analysis of T–S Fuzzy Control Systems by Using Set Theory , 2015, IEEE Transactions on Fuzzy Systems.

[19]  Jin Bae Park,et al.  Approaches to extended non-quadratic stability and stabilization conditions for discrete-time Takagi-Sugeno fuzzy systems , 2011, Autom..

[20]  Baocang Ding,et al.  Homogeneous Polynomially Nonquadratic Stabilization of Discrete-Time Takagi–Sugeno Systems via Nonparallel Distributed Compensation Law , 2010, IEEE Transactions on Fuzzy Systems.

[21]  Hamid Reza Karimi,et al.  Robust Unknown Input Observer Design for Linear Uncertain Time Delay Systems with Application to Fault Detection , 2014 .

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

[23]  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.

[24]  Thierry-Marie Guerra,et al.  LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form , 2004, Autom..

[25]  Jin Bae Park,et al.  Further improvement of periodic control approach for relaxed stabilization condition of discrete-time Takagi-Sugeno fuzzy systems , 2011, Fuzzy Sets Syst..

[26]  Tao Zou,et al.  Asymptotically necessary and sufficient stability conditions for discrete-time Takagi-Sugeno model: Extended applications of Polya's theorem and homogeneous polynomials , 2014, J. Frankl. Inst..

[27]  Ricardo C. L. F. Oliveira,et al.  Parameter-Dependent LMIs in Robust Analysis: Characterization of Homogeneous Polynomially Parameter-Dependent Solutions Via LMI Relaxations , 2007, IEEE Transactions on Automatic Control.