Delay-Range-Dependent Stability Criteria for Takagi-Sugeno Fuzzy Systems with Fast Time-Varying Delays

The problem of delay-range-dependent stability for T-S fuzzy system with interval time-varying delay is investigated. The constraint on the derivative of the time-varying delay is not required, which allows the time delay to be a fast time-varying function. By developing delay decomposition approach, integral inequalities approach (IIA), and Leibniz-Newton formula, the information of the delayed plant states can be taken into full consideration, and new delay-dependent sufficient stability criteria are obtained in terms of linear matrix inequalities (LMIs) which can be easily solved by various optimization algorithms. Simulation examples show resulting criteria outperform all existing ones in the literature. It is worth pointing out that our criteria are carried out more efficiently for computation and less conservatism of the proposed criteria.

[1]  Engang Tian,et al.  Delay-dependent stability analysis and synthesis of uncertain T-S fuzzy systems with time-varying delay , 2006, Fuzzy Sets Syst..

[2]  X. Liao,et al.  Delay-dependent robust stability of uncertain fuzzy systems with time-varying delays , 2004 .

[3]  Xin-Ping Guan,et al.  Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays , 2004, IEEE Transactions on Fuzzy Systems.

[4]  Pin-Lin Liu,et al.  Robust exponential stability for uncertain time-varying delay systems with delay dependence , 2009, J. Frankl. Inst..

[5]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[6]  Jinhui Zhang,et al.  New Robust Stability Criterion for Uncertain Fuzzy Systems with Fast Time-Varying Delays , 2006, FSKD.

[7]  Shaocheng Tong,et al.  Delay-dependent stability analysis and control synthesis of fuzzy dynamic systems with time delay , 2006, Fuzzy Sets Syst..

[8]  Guilin Wen,et al.  Improved stability criteria for time-varying delayed T-S fuzzy systems via delay partitioning approach , 2011, Fuzzy Sets Syst..

[9]  Guan Xinping.  Fuzzy guaranteed cost control for nonlinear systems with time-varying delay , 2007 .

[10]  D. D. Perlmutter,et al.  Stability of time‐delay systems , 1972 .

[11]  Engang Tian,et al.  Improved delay-dependent robust stabilization conditions of uncertain T-S fuzzy systems with time-varying delay , 2008, Fuzzy Sets Syst..

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

[13]  Xingwen Liu.  Delay-dependent H∞ control for uncertain fuzzy systems with time-varying delays , 2008 .

[14]  Guang-Hong Yang,et al.  New results of stability analysis for systems with time‐varying delay , 2010 .

[15]  C. Lien.  Further results on delay-dependent robust stability of uncertain fuzzy systems with time-varying delay , 2006 .

[16]  Shaocheng Tong,et al.  New delay-dependent stabilization conditions of T-S fuzzy systems with constant delay , 2007, Fuzzy Sets Syst..

[17]  C. Peng,et al.  On Delay-dependent Robust Stability Criteria for Uncertain T-S Fuzzy Systems with Interval Time-varying Delay , 2011 .

[18]  Z. Zuo,et al.  Robust stability and stabilisation for nonlinear uncertain time-delay systems via fuzzy control approach , 2007 .

[19]  Dong Yue,et al.  Delay-dependent robust Hinfinity control for T-S fuzzy system with interval time-varying delay , 2009, Fuzzy Sets Syst..

[20]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[21]  Yupu Yang,et al.  New delay‐dependent stability analysis and synthesis of T–S fuzzy systems with time‐varying delay , 2010 .

[22]  Fernando de Oliveira Souza,et al.  On Stability and Stabilization of T–S Fuzzy Time-Delayed Systems , 2009, IEEE Transactions on Fuzzy Systems.

[23]  L. Mozelli,et al.  A new discretized Lyapunov–Krasovskii functional for stability analysis and control design of time‐delayed TS fuzzy systems , 2011 .

[24]  Guang-Hong Yang,et al.  Jensen inequality approach to stability analysis of discrete-time systems with time-varying delay , 2008, 2008 American Control Conference.

[25]  Jun Yoneyama,et al.  Robust stability and stabilization for uncertain Takagi-Sugeno fuzzy time-delay systems , 2007, Fuzzy Sets Syst..

[26]  Han-Xiong Li,et al.  New Approach to Delay-Dependent Stability Analysis and Stabilization for Continuous-Time Fuzzy Systems With Time-Varying Delay , 2007, IEEE Transactions on Fuzzy Systems.

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

[28]  Huaguang Zhang,et al.  Novel Weighting-Delay-Based Stability Criteria for Recurrent Neural Networks With Time-Varying Delay , 2010, IEEE Transactions on Neural Networks.

[29]  Ju H. Park,et al.  Augmented Lyapunov-Krasovskii functional approaches to robust stability criteria for uncertain Takagi-Sugeno fuzzy systems with time-varying delays , 2012, Fuzzy Sets Syst..

[30]  Cees J. Koomen.  The entropy of design: A study on the meaning of creativity , 1985, IEEE Transactions on Systems, Man, and Cybernetics.