New Stability Criterion for Continuous-Time Takagi–Sugeno Fuzzy Systems With Time-Varying Delay

In this technical paper, a new Lyapunov–Krasovskii functional (LKF) is designed to study the stability of continuous-time Takagi–Sugeno fuzzy systems with time-varying delay. The integrand of the LKF depends on integral variable and time <inline-formula> <tex-math notation="LaTeX">${t}$ </tex-math></inline-formula> which can help to reduce the number of linear matrix inequalities (LMIs). Then, a new stability criterion is derived by analyzing the sign of the time derivatives of membership functions. Compared with the existing results, larger delay bounds can be obtained by applying the new criterion. In the end, two examples show the effectiveness of the conclusions.

[1]  Minrui Fei,et al.  An improved result on the stability of uncertain T-S fuzzy systems with interval time-varying delay , 2013, Fuzzy Sets Syst..

[2]  Huaguang Zhang,et al.  Leader-Based Optimal Coordination Control for the Consensus Problem of Multiagent Differential Games via Fuzzy Adaptive Dynamic Programming , 2015, IEEE Transactions on Fuzzy Systems.

[3]  Y. Wang,et al.  Stability Analysis of Markovian Jumping Stochastic Cohen–Grossberg Neural Networks With Mixed Time Delays , 2008, IEEE Transactions on Neural Networks.

[4]  Fernando de Oliveira Souza,et al.  On delay-dependent stability conditions for Takagi-Sugeno fuzzy systems , 2014, J. Frankl. Inst..

[5]  Yongduan Song,et al.  A novel approach to output feedback control of fuzzy stochastic systems , 2014, Autom..

[6]  Xiaodi Li,et al.  Stabilization of Delay Systems: Delay-Dependent Impulsive Control , 2017, IEEE Transactions on Automatic Control.

[7]  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..

[8]  Xiaodi Li,et al.  Stability of nonlinear differential systems with state-dependent delayed impulses , 2016, Autom..

[9]  Yongduan Song,et al.  Fault Detection Filtering for Nonlinear Switched Stochastic Systems , 2016, IEEE Transactions on Automatic Control.

[10]  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.

[11]  Wei Xing Zheng,et al.  Improved Stability Condition for Takagi–Sugeno Fuzzy Systems With Time-Varying Delay , 2017, IEEE Transactions on Cybernetics.

[12]  Tong Heng Lee,et al.  LMI Approach to Analysis and Control of Takagi-Sugeno Fuzzy Systems with Time Delay (Lecture Notes in Control and Information Sciences) , 2007 .

[13]  Xiaodong Liu,et al.  New approaches on Hinfinity control of T-S fuzzy systems with interval time-varying delay , 2009, Fuzzy Sets Syst..

[14]  Peng Shi,et al.  Reliable Mixed $H_\infty $ and Passivity-Based Control for Fuzzy Markovian Switching Systems With Probabilistic Time Delays and Actuator Failures , 2015, IEEE Transactions on Cybernetics.

[15]  Hak-Keung Lam,et al.  A New Approach to Stability and Stabilization Analysis for Continuous-Time Takagi–Sugeno Fuzzy Systems With Time Delay , 2018, IEEE Transactions on Fuzzy Systems.

[16]  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.

[17]  H. Piaggio.  Mathematical Analysis , 1955, Nature.

[18]  Hamid Reza Karimi,et al.  Robust Stability and Stabilization of Uncertain T–S Fuzzy Systems With Time-Varying Delay: An Input–Output Approach , 2013, IEEE Transactions on Fuzzy Systems.

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

[20]  Ju H. Park,et al.  Stability and stabilization of T-S fuzzy systems with time-varying delays via augmented Lyapunov-Krasovskii functionals , 2016, Inf. Sci..

[21]  Frédéric Gouaisbaut,et al.  Wirtinger-based integral inequality: Application to time-delay systems , 2013, Autom..

[22]  Dong Yue,et al.  Control Synthesis of Discrete-Time T–S Fuzzy Systems: Reducing the Conservatism Whilst Alleviating the Computational Burden , 2017, IEEE Transactions on Cybernetics.