Finite-frequency model reduction of discrete-time T-S fuzzy state-delay systems

This paper is concerned with the problem of model reduction for discrete-time Takagi-Sugeno (T-S) fuzzy state-delay systems with finite-frequency input signals. A new finite-frequency model reduction algorithm is proposed, which can get a better approximation performance than the existing full-frequency methods. Firstly, a finite-frequency H ∞ performance index is defined in the frequency domain. Then, a stability condition and a finite-frequency H ∞ performance analysis condition are developed by the aid of Jensen's inequality and Parseval's theorem, respectively. Based on these conditions, sufficient model reduction conditions are derived for discrete-time T-S fuzzy state-delay systems. An optimization algorithm is proposed to obtain a stable reduced-order model satisfying the finite-frequency performance specification. Finally, the effectiveness of the proposed method is illustrated by a numerical example.

[1]  Ya-Jun Pan,et al.  Mean-Square Exponential Stability and Stabilisation of Stochastic Singular Systems with Multiple Time-Varying Delays , 2014, Circuits, Systems, and Signal Processing.

[2]  Renquan Lu,et al.  Networked Control With State Reset and Quantized Measurements: Observer-Based Case , 2013, IEEE Transactions on Industrial Electronics.

[3]  Athanasios C. Antoulas,et al.  Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control) , 2005 .

[4]  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.

[5]  Bashir Ahmad,et al.  Model reduction of A class of Markov jump nonlinear systems with time-varying delays via projection approach , 2015, Neurocomputing.

[6]  Hak-Keung Lam,et al.  Model reduction for interval type-2 Takagi-Sugeno fuzzy systems , 2015, Autom..

[7]  Peng Shi,et al.  Input—Output Approach to Control for Fuzzy Markov Jump Systems With Time-Varying Delays and Uncertain Packet Dropout Rate , 2015, IEEE Transactions on Cybernetics.

[8]  Mingyu Wang,et al.  Approximation-Based Adaptive Tracking Control for MIMO Nonlinear Systems With Input Saturation , 2015, IEEE Transactions on Cybernetics.

[9]  Guang-Hong Yang,et al.  H∞ model reduction of linear continuous-time systems over finite frequency interval-LMI based approach , 2009, 2009 American Control Conference.

[10]  Shaocheng Tong,et al.  Adaptive Fuzzy Control for a Class of Nonlinear Discrete-Time Systems With Backlash , 2014, IEEE Transactions on Fuzzy Systems.

[11]  Shaocheng Tong,et al.  Adaptive Fuzzy Identification and Control for a Class of Nonlinear Pure-Feedback MIMO Systems With Unknown Dead Zones , 2015, IEEE Transactions on Fuzzy Systems.

[12]  Jianjun Bai,et al.  New delay-dependent robust stability criteria for uncertain neutral systems with mixed delays , 2014, J. Frankl. Inst..

[13]  Dong Yue,et al.  Further Studies on Control Synthesis of Discrete-Time T-S Fuzzy Systems via Augmented Multi-Indexed Matrix Approach , 2014, IEEE Transactions on Cybernetics.

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

[15]  Hyunjoong Kim,et al.  Functional Analysis I , 2017 .

[16]  Shun-Hung Tsai,et al.  A novel stabilization condition for a class of T-S fuzzy time-delay systems , 2016, Neurocomputing.

[17]  Guang-Hong Yang,et al.  Control Synthesis of T–S Fuzzy Systems Based on a New Control Scheme , 2011, IEEE Transactions on Fuzzy Systems.

[18]  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.

[19]  Xiaoli Li,et al.  Finite-Frequency Model Reduction of Two-Dimensional Digital Filters , 2015, IEEE Transactions on Automatic Control.

[20]  Hak-Keung Lam,et al.  Observer-Based Fuzzy Control for Nonlinear Networked Systems Under Unmeasurable Premise Variables , 2016, IEEE Transactions on Fuzzy Systems.

[21]  Jian-Ning Li,et al.  Mean-square exponential stability for stochastic discrete-time recurrent neural networks with mixed time delays , 2015, Neurocomputing.

[22]  Jie Zhang,et al.  H∞ state estimation for discrete-time delayed neural networks with randomly occurring quantizations and missing measurements , 2015, Neurocomputing.

[23]  Guang-Hong Yang,et al.  H∞ model reduction of linear continuous-time systems over finite frequency interval-LMI based approach , 2009, ACC.

[24]  Yan Shi,et al.  Switched Fuzzy Output Feedback Control and Its Application to a Mass–Spring–Damping System , 2016, IEEE Transactions on Fuzzy Systems.

[25]  Guang-Hong Yang,et al.  Delay‐dependent filtering for discrete‐time state‐delayed systems with small gain conditions in finite frequency ranges , 2011 .

[26]  A. Antoulas,et al.  A Survey of Model Reduction by Balanced Truncation and Some New Results , 2004 .

[27]  Guo-Ping Liu,et al.  Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays , 2004, Syst. Control. Lett..

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

[29]  Karl-Erik Årzén,et al.  Piecewise quadratic stability of fuzzy systems , 1999, IEEE Trans. Fuzzy Syst..

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

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

[32]  Renquan Lu,et al.  Asynchronous Dissipative State Estimation for Stochastic Complex Networks With Quantized Jumping Coupling and Uncertain Measurements , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[33]  Fuad E. Alsaadi,et al.  Almost sure H∞ sliding mode control for nonlinear stochastic systems with Markovian switching and time-delays , 2016, Neurocomputing.

[34]  Athanasios C. Antoulas,et al.  Approximation of Large-Scale Dynamical Systems , 2005, Advances in Design and Control.

[35]  Xun-lin Zhu,et al.  New stability criterion for linear switched systems with time‐varying delay , 2014 .

[36]  Shaocheng Tong,et al.  Composite Adaptive Fuzzy Output Feedback Control Design for Uncertain Nonlinear Strict-Feedback Systems With Input Saturation , 2015, IEEE Transactions on Cybernetics.

[37]  Li Li,et al.  Robust stabilization of T-S fuzzy discrete systems with actuator saturation via PDC and non-PDC law , 2015, Neurocomputing.

[38]  Shinji Hara,et al.  Generalized KYP lemma: unified frequency domain inequalities with design applications , 2005, IEEE Transactions on Automatic Control.

[39]  Huijun Gao,et al.  Passivity-preserving model reduction with finite frequency H∞ approximation performance , 2014, Autom..

[40]  Yongduan Song,et al.  ${\cal H}_{\infty}$ Model Reduction of Takagi–Sugeno Fuzzy Stochastic Systems , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[41]  K. Glover.  All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds† , 1984 .

[42]  G. Lastman.  Reduced-order aggregated models for bilinear time-invariant dynamical systems , 1984 .

[43]  B. Moore.  Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .

[44]  Kazuo Tanaka,et al.  Stability analysis and design of fuzzy control systems , 1992 .