Sliding Mode Control for Fuzzy Singular Systems With Time Delay Based on Vector Integral Sliding Mode Surface

This article studies the sliding mode control (SMC) of a class of Takagi–Sugeno (T–S) fuzzy singular systems with matched external disturbances. The key advantage of this article is that the input matrices of the considered fuzzy systems could be different, and a novel SMC provided in this article has strong robustness. In this article, systems with delayed state are considered. The time delay is a known constant, and the full state vector is available for feedback. At first, a new sliding mode surface, vector integral sliding mode surface, is proposed. By use of this surface, the stabilization problem for some T–S fuzzy singular systems with different input matrices can be settled. Second, a new SMC law is provided to avoid the state of the considered fuzzy system escaping from every subsliding mode surface. Finally, two examples are provided to verify the validity of the method proposed in this article.

[1]  Zhiyu Xi,et al.  A New Design of Robust ${\rm H}_{\infty}$ Sliding Mode Control for Uncertain Stochastic T-S Fuzzy Time-Delay Systems , 2014, IEEE Transactions on Cybernetics.

[2]  Xing-Gang Yan,et al.  Robust Stabilization of T–S Fuzzy Stochastic Descriptor Systems via Integral Sliding Modes , 2018, IEEE Transactions on Cybernetics.

[3]  Dong Yue,et al.  Multi-Instant Observer Design of Discrete-Time Fuzzy Systems: A Ranking-Based Switching Approach , 2017, IEEE Transactions on Fuzzy Systems.

[4]  Ligang Wu,et al.  Event-triggered fuzzy control of nonlinear systems with its application to inverted pendulum systems , 2018, Autom..

[5]  Qiuye Sun,et al.  The initial guess estimation newton method for power flow in distribution systems , 2017, IEEE/CAA Journal of Automatica Sinica.

[6]  Irfan Yazici,et al.  Fast and robust voltage control of DC–DC boost converter by using fast terminal sliding mode controller , 2016 .

[7]  Qingling Zhang,et al.  Finite-time synchronization for second-order nonlinear multi-agent system via pinning exponent sliding mode control. , 2016, ISA transactions.

[8]  Wei Xing Zheng,et al.  Dynamic Event-Based Control of Nonlinear Stochastic Systems , 2017, IEEE Transactions on Automatic Control.

[9]  Jun Hu,et al.  Sliding mode control for uncertain discrete-time systems with Markovian jumping parameters and mixed delays , 2014, J. Frankl. Inst..

[10]  Marcelo C. M. Teixeira,et al.  Stabilizing controller design for uncertain nonlinear systems using fuzzy models , 1999, IEEE Trans. Fuzzy Syst..

[11]  Li Li,et al.  Sliding mode control for singular stochastic Markovian jump systems with uncertainties , 2017, Autom..

[12]  Christopher Edwards,et al.  Variable Structure Control of Complex Systems: Analysis and Design , 2016 .

[13]  Kazuo Tanaka,et al.  Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach , 2008 .

[14]  Camila Lobo Coutinho,et al.  Output-feedback sliding-mode control of multivariable systems with uncertain time-varying state delays and unmatched non-linearities , 2013 .

[15]  Xing-Gang Yan,et al.  Observer-Based Fuzzy Integral Sliding Mode Control For Nonlinear Descriptor Systems , 2018, IEEE Transactions on Fuzzy Systems.

[16]  Wei Xing Zheng,et al.  Passivity-based sliding mode control of uncertain singular time-delay systems , 2009, Autom..

[17]  Huaguang Zhang,et al.  Global Asymptotic Stability of Recurrent Neural Networks With Multiple Time-Varying Delays , 2008, IEEE Transactions on Neural Networks.

[18]  Yuanyuan Zhang,et al.  An analysis of the stability and chattering reduction of high-order sliding mode tracking control for a hypersonic vehicle , 2016, Inf. Sci..

[19]  E. Uezato,et al.  Strict LMI conditions for stability, robust stabilization, and H/sub /spl infin// control of descriptor systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[20]  V. Utkin,et al.  Integral sliding mode in systems operating under uncertainty conditions , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

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

[22]  Qingling Zhang,et al.  Sliding-Mode Control for Singular Markovian Jump Systems With Brownian Motion Based on Stochastic Sliding Mode Surface , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[23]  Zhigang Zeng,et al.  Fuzzy Control for Uncertain Vehicle Active Suspension Systems via Dynamic Sliding-Mode Approach , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[24]  Qingling Zhang,et al.  Novel sliding surface design for nonlinear singular systems , 2016, Neurocomputing.

[25]  Huaguang Zhang,et al.  A Novel Infinite-Time Optimal Tracking Control Scheme for a Class of Discrete-Time Nonlinear Systems via the Greedy HDP Iteration Algorithm , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[26]  Chunyu Yang,et al.  Stabilization of singular Markovian jump systems with time-varying switchings , 2015, Inf. Sci..

[27]  Liang Qiao,et al.  Admissibility Analysis and Control Synthesis for T–S Fuzzy Descriptor Systems , 2017, IEEE Transactions on Fuzzy Systems.

[28]  Huaguang Zhang,et al.  An SOS-Based Observer Design for Discrete-Time Polynomial Fuzzy Systems , 2015, Int. J. Fuzzy Syst..

[29]  Jianbin Qiu,et al.  Universal Fuzzy Integral Sliding-Mode Controllers Based on T–S Fuzzy Models , 2014, IEEE Transactions on Fuzzy Systems.

[30]  Huaguang Zhang,et al.  Observer-based H∞ fuzzy control for modified repetitive control systems , 2018, Neurocomputing.

[31]  Yongduan Song,et al.  Descriptor sliding mode approach for fault/noise reconstruction and fault-tolerant control of nonlinear uncertain systems , 2016, Inf. Sci..

[32]  Huaguang Zhang,et al.  Dissipativity Analysis and Synthesis for a Class of T–S Fuzzy Descriptor Systems , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[33]  Huaguang Zhang,et al.  Multilevel feature moving average ratio method for fault diagnosis of the microgrid inverter switch , 2017, IEEE/CAA Journal of Automatica Sinica.

[34]  Yi Zhang,et al.  H∞ control of T-S fuzzy fish population logistic model with the invasion of alien species , 2016, Neurocomputing.

[35]  Huaguang Zhang,et al.  Networked Synchronization Control of Coupled Dynamic Networks With Time-Varying Delay , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[37]  Huaguang Zhang,et al.  Sensor Fault Estimation of Switched Fuzzy Systems With Unknown Input , 2018, IEEE Transactions on Fuzzy Systems.

[38]  Mihai Comanescu.  Design and Implementation of a Highly Robust Sensorless Sliding Mode Observer for the Flux Magnitude of the Induction Motor , 2016, IEEE Transactions on Energy Conversion.

[39]  Qingling Zhang,et al.  A linear switching function approach to sliding mode control and observation of descriptor systems , 2018, Autom..

[40]  Qingling Zhang,et al.  A new design of sliding mode control for Markovian jump systems based on stochastic sliding surface , 2017, Inf. Sci..

[41]  Yong Wang,et al.  Robust ${\mathscr H}_{\infty }$ Control of T–S Fuzzy Time-Delay Systems via a New Sliding-Mode Control Scheme , 2014, IEEE Transactions on Fuzzy Systems.

[42]  Hak-Keung Lam,et al.  Adaptive Sliding Mode Control for Interval Type-2 Fuzzy Systems , 2016, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[43]  Zhihong Man,et al.  Robust Control of a Vehicle Steer-by-Wire System Using Adaptive Sliding Mode , 2016, IEEE Transactions on Industrial Electronics.

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

[45]  Shengyuan Xu,et al.  Robust Control and Filtering of Singular Systems , 2006 .

[46]  Ligang Wu,et al.  Sliding mode control of T-S fuzzy descriptor systems with time-delay , 2012, J. Frankl. Inst..

[47]  Chih-Chiang Chen,et al.  Study of Nonsingular Fast Terminal Sliding-Mode Fault-Tolerant Control , 2015, IEEE Transactions on Industrial Electronics.

[48]  Shuzhi Sam Ge,et al.  Robust Fault-Tolerant Control for a Class of Second-Order Nonlinear Systems Using an Adaptive Third-Order Sliding Mode Control , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.