Robust H∞ stabilization for T-S fuzzy systems with time-varying delays and memory sampled-data control

Abstract In this paper, we address the robust H ∞ stabilization for T-S fuzzy systems with time-varying delays based on memory sampled-data control. By developing some new terms, an improved piecewise Lyapunov–Krasovskii functional (LKF) is constructed to take full advantage of characteristic about real sampling pattern. Furthermore, some relaxed matrices proposed in the LKF are not necessarily positive definite. By using the LKF and Free-Matrix-Based (FMB) integral inequality, some sufficient criteria are established to ensure the stability of fuzzy systems and reduce the influence of external disturbance with an H ∞ norm bound. Then, the memory sampled-data controller can be derived by solving a group of linear matrix inequalities (LMIs) with the maximal sampling period. Finally, a numerical example is given to demonstrate the benefits and the superiority of the approach proposed.

[1]  Hamid Reza Karimi,et al.  An Improved Result on Exponential Stabilization of Sampled-Data Fuzzy Systems , 2018, IEEE Transactions on Fuzzy Systems.

[2]  Saeid Nahavandi,et al.  New delay range–dependent stability criteria for interval time‐varying delay systems via Wirtinger‐based inequalities , 2018 .

[3]  Xin-Ping Guan,et al.  Decentralized event-triggered control for interconnected time-delay stochastic nonlinear systems using neural networks , 2018, Neurocomputing.

[4]  Changchun Hua,et al.  Bayesian Block Structure Sparse Based T–S Fuzzy Modeling for Dynamic Prediction of Hot Metal Silicon Content in the Blast Furnace , 2018, IEEE Transactions on Industrial Electronics.

[5]  Saeid Nahavandi,et al.  Improved delay-dependent stability criteria for neutral systems with mixed interval time-varying delays and nonlinear disturbances , 2017, J. Frankl. Inst..

[6]  Ju H. Park,et al.  Stability Analysis of Sampled-Data Systems via Free-Matrix-Based Time-Dependent Discontinuous Lyapunov Approach , 2017, IEEE Transactions on Automatic Control.

[7]  Ju H. Park,et al.  Further Results on Stabilization of Chaotic Systems Based on Fuzzy Memory Sampled-Data Control , 2018, IEEE Transactions on Fuzzy Systems.

[8]  Min Wu,et al.  New Delay-dependent Stability Criteria for T-S Fuzzy Systems with a Time-varying Delay , 2008 .

[9]  Jin Bae Park,et al.  Decentralized sampled-data H∞ fuzzy filter for nonlinear large-scale systems , 2015, Fuzzy Sets Syst..

[10]  Jun Cheng,et al.  Fuzzy-model-based H∞ control for discrete-time switched systems with quantized feedback and unreliable links , 2018, Inf. Sci..

[11]  Engang Tian,et al.  Sampled-data robust H∞ control for T-S fuzzy systems with time delay and uncertainties , 2011, Fuzzy Sets Syst..

[12]  Hamid Reza Karimi,et al.  A Flexible Terminal Approach to Sampled-Data Exponentially Synchronization of Markovian Neural Networks With Time-Varying Delayed Signals , 2018, IEEE Transactions on Cybernetics.

[13]  Hamid Reza Karimi,et al.  A computational method for solving optimal control and parameter estimation of linear systems using Haar wavelets , 2004, Int. J. Comput. Math..

[14]  Yonggui Kao,et al.  Stability and Stabilization for Singular Switching Semi-Markovian Jump Systems With Generally Uncertain Transition Rates , 2018, IEEE Transactions on Automatic Control.

[15]  Jun Yoneyama,et al.  Robust H∞ control of uncertain fuzzy systems under time-varying sampling , 2010, Fuzzy Sets Syst..

[16]  Shengyuan Xu,et al.  Slow State Variables Feedback Stabilization for Semi-Markov Jump Systems With Singular Perturbations , 2018, IEEE Transactions on Automatic Control.

[17]  Hamid Reza Karimi,et al.  Distributed $H_\infty$ Output-Feedback Control for Consensus of Heterogeneous Linear Multiagent Systems With Aperiodic Sampled-Data Communications , 2018, IEEE Transactions on Industrial Electronics.

[18]  Hamid Reza Karimi,et al.  $\mathscr {L}_\infty$ Control for Positive Delay Systems With Semi-Markov Process and Application to a Communication Network Model , 2019, IEEE Transactions on Industrial Electronics.

[19]  Changchun Hua,et al.  Output feedback NN tracking control for fractional-order nonlinear systems with time-delay and input quantization , 2018, Neurocomputing.

[20]  Hak-Keung Lam,et al.  Fuzzy Sampled-Data Control for Uncertain Vehicle Suspension Systems , 2014, IEEE Transactions on Cybernetics.

[21]  Hao Shen,et al.  Recent Advances in Control and Filtering of Dynamic Systems with Constrained Signals , 2018, Studies in Systems, Decision and Control.

[22]  Shouming Zhong,et al.  A New Approach to Stabilization of Chaotic Systems With Nonfragile Fuzzy Proportional Retarded Sampled-Data Control , 2019, IEEE Transactions on Cybernetics.

[23]  Young Hoon Joo,et al.  Intelligent digital redesign for non-linear systems: observer-based sampled-data fuzzy control approach , 2016 .

[24]  Tao Li,et al.  Robust stability for neural networks with time-varying delays and linear fractional uncertainties , 2007, Neurocomputing.

[25]  Ho Jae Lee,et al.  Direct discrete-time design approach to robust sampled-data observer-based output-feedback fuzzy control , 2016, Int. J. Syst. Sci..

[26]  Shouming Zhong,et al.  Event-triggered sampling control for stability and stabilization of memristive neural networks with communication delays , 2017, Appl. Math. Comput..

[27]  Jing Wang,et al.  Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback , 2018, Appl. Math. Comput..

[28]  Hamid Reza Karimi,et al.  Data-driven design of robust fault detection system for wind turbines , 2014 .

[29]  Hamid Reza Karimi,et al.  Resilient Sampled-Data Control for Markovian Jump Systems With an Adaptive Fault-Tolerant Mechanism , 2017, IEEE Transactions on Circuits and Systems II: Express Briefs.

[30]  Wei Xing Zheng,et al.  Second-Order Sliding-Mode Controller Design and Its Implementation for Buck Converters , 2018, IEEE Transactions on Industrial Informatics.

[31]  Shouming Zhong,et al.  Sampled-data synchronization of chaotic Lur'e systems via input-delay-dependent-free-matrix zero equality approach , 2017, Appl. Math. Comput..

[32]  Wenhai Qi,et al.  Observer-Based Adaptive SMC for Nonlinear Uncertain Singular Semi-Markov Jump Systems With Applications to DC Motor , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

[33]  PooGyeon Park,et al.  Reciprocally convex approach to stability of systems with time-varying delays , 2011, Autom..

[34]  H. Karimi,et al.  Discrete‐time H −  ∕ H ∞  sensor fault detection observer design for nonlinear systems with parameter uncertainty , 2015 .

[35]  Zhenbin Du,et al.  Fuzzy Robust H∞ Sampled-Data Control for Uncertain Nonlinear Systems with Time-Varying Delay , 2016, International Journal of Fuzzy Systems.

[36]  Shihua Li,et al.  Prescribed-Time Second-Order Sliding Mode Controller Design Subject to Mismatched Term , 2017, IEEE Transactions on Circuits and Systems II: Express Briefs.

[37]  Huai-Ning Wu,et al.  On Fuzzy Sampled-Data Control of Chaotic Systems Via a Time-Dependent Lyapunov Functional Approach , 2015, IEEE Transactions on Cybernetics.

[38]  Xin-Ping Guan,et al.  Decentralized adaptive tracking quantized control for interconnected pure feedback time delay nonlinear systems , 2018, J. Frankl. Inst..

[39]  Hamid Reza Karimi,et al.  Sampled-Data Control of Network Systems in Industrial Manufacturing , 2018, IEEE Transactions on Industrial Electronics.

[40]  Xinzhi Liu,et al.  A novel approach to stability and stabilization of fuzzy sampled-data Markovian chaotic systems , 2017, Fuzzy Sets Syst..

[41]  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..

[42]  Feng Shu,et al.  Robust H∞ control of T-S fuzzy systems with input time-varying delays: A delay partitioning method , 2018, Appl. Math. Comput..

[43]  Dong Yue,et al.  An Improved Input Delay Approach to Stabilization of Fuzzy Systems Under Variable Sampling , 2012, IEEE Transactions on Fuzzy Systems.

[44]  Yajuan Liu,et al.  Stability and Stabilization of Takagi–Sugeno Fuzzy Systems via Sampled-Data and State Quantized Controller , 2016, IEEE Transactions on Fuzzy Systems.