Robust Adaptive Sliding Mode Observer Design for T-S Fuzzy Descriptor Systems With Time-Varying Delay

This paper addresses the problems of robust adaptive sliding mode observer (SMO) design and SMO-based sliding mode control (SMC) for T-S fuzzy descriptor systems with time-varying delay. Until now, there are a few results about the adaptive SMO design problem and adaptive SMO-based SMC for T-S fuzzy descriptor systems with time-varying delay. Therefore, we are motivated to study this issue. First, two integral-type sliding surfaces, which involve the SMO gain matrix, are constructed for the error system and the SMO system, respectively. Then, some delay-dependent sufficient conditions are established, such that the sliding motions are robustly admissible with $H\infty $ performance. New adaptive sliding mode controllers, which need not to use the assumption that the fast subsystem of descriptor system is observable, are synthesized for the error system and the SMO system, such that the reachability conditions can be guaranteed. In addition, the adaptive control strategy is applied to estimate the unknown parameters. Finally, simulation examples are discussed to show the effectiveness of our approach.

[1]  Qingling Zhang,et al.  Integral Sliding Mode Control for Markovian Jump T-S Fuzzy Descriptor Systems Based on the Super-Twisting Algorithm , 2017 .

[2]  Xian Zhang,et al.  Fuzzy-Model-Based ${{\cal D}}$-Stability and Nonfragile Control for Discrete-Time Descriptor Systems With Multiple Delays , 2014, IEEE Transactions on Fuzzy Systems.

[3]  Yingying Wang,et al.  Robust Sliding-Mode Control for Fuzzy Stochastic Singular Systems With Different Local Input Matrices , 2018, IEEE Access.

[4]  Tianyou Chai,et al.  Observer design for a class of nonlinear descriptor systems , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[5]  Thierry-Marie Guerra,et al.  Observer design for Takagi-Sugeno descriptor models: An LMI approach , 2015, Autom..

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

[7]  Wei Li,et al.  A novel fuzzy integral sliding mode current control strategy for maximizing wind power extraction and eliminating voltage harmonics , 2015 .

[8]  Christopher Edwards,et al.  Adaptive Sliding-Mode-Observer-Based Fault Reconstruction for Nonlinear Systems With Parametric Uncertainties , 2008, IEEE Transactions on Industrial Electronics.

[9]  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.

[10]  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.

[11]  Qingling Zhang,et al.  Robust H∞ sliding mode observer design for a class of Takagi-Sugeno fuzzy descriptor systems with time-varying delay , 2018, Appl. Math. Comput..

[12]  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.

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

[14]  Christopher Edwards,et al.  Sliding Mode Control and Observation , 2013 .

[15]  Hamid Reza Karimi,et al.  Adaptive Sliding Mode Control for Takagi–Sugeno Fuzzy Systems and Its Applications , 2018, IEEE Transactions on Fuzzy Systems.

[16]  Wei Li,et al.  Fuzzy-Logic Sliding-Mode Control Strategy for Extracting Maximum Wind Power , 2015, IEEE Transactions on Energy Conversion.

[17]  Mohamed Darouach,et al.  Observers and Observer-Based Control for Descriptor Systems Revisited , 2014, IEEE Transactions on Automatic Control.

[18]  Yonggui Kao,et al.  A Novel Robust Fuzzy Integral Sliding Mode Control for Nonlinear Semi-Markovian Jump T–S Fuzzy Systems , 2018, IEEE Transactions on Fuzzy Systems.

[19]  Jianbin Qiu,et al.  Robust $\mathscr{H}_{\infty }$ Control for Stochastic T–S Fuzzy Systems via Integral Sliding-Mode Approach , 2014, IEEE Transactions on Fuzzy Systems.

[20]  Ligang Wu,et al.  Observer-based adaptive sliding mode control for nonlinear Markovian jump systems , 2016, Autom..

[21]  Bing Chen,et al.  Observer-Based Adaptive Fuzzy Control for a Class of Nonlinear Delayed Systems , 2016, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[22]  I. Petersen.  A stabilization algorithm for a class of uncertain linear systems , 1987 .

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

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

[25]  Christopher Edwards,et al.  Sliding mode control for time-varying delayed systems based on a reduced-order observer , 2010, Autom..

[26]  Renquan Lu,et al.  New stability and stabilization criteria for a class of fuzzy singular systems with time-varying delay , 2014, J. Frankl. Inst..

[27]  H. Gassara,et al.  Dissipativity-based integral sliding-mode control for a class of Takagi–Sugeno fuzzy singular systems with time-varying delay , 2014 .

[28]  Chee Pin Tan,et al.  An LMI approach for designing sliding mode observers , 2001 .

[29]  Wen Chen,et al.  Fault Reconstruction and Fault-Tolerant Control via Learning Observers in Takagi–Sugeno Fuzzy Descriptor Systems With Time Delays , 2015, IEEE Transactions on Industrial Electronics.

[30]  Hongbin Zhang,et al.  Delay-dependent stability and Hinfinity control for a class of fuzzy descriptor systems with time-delay , 2009, Fuzzy Sets Syst..

[31]  Shengyuan Xu,et al.  Robust stability and stabilization for singular systems with state delay and parameter uncertainty , 2002, IEEE Trans. Autom. Control..

[32]  Christopher Edwards,et al.  Sliding mode observers for robust detection and reconstruction of actuator and sensor faults , 2003 .

[33]  Shengyuan Xu,et al.  Robust admissibility of time-varying singular systems with commensurate time delays , 2009, Autom..

[34]  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.

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

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

[37]  Yuanqing Xia,et al.  Robust Adaptive Sliding-Mode Control for Fuzzy Systems With Mismatched Uncertainties , 2010, IEEE Transactions on Fuzzy Systems.

[38]  Yonggui Kao,et al.  Passification of Uncertain Singular Semi-Markovian Jump Systems With Actuator Failures Via Sliding Mode Approach , 2017, IEEE Transactions on Automatic Control.

[39]  C. Edwards,et al.  Fault estimation for single output nonlinear systems using an adaptive sliding mode estimator , 2008 .

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

[41]  Jianbin Qiu,et al.  Descriptor reduced-order sliding mode observers design for switched systems with sensor and actuator faults , 2017, Autom..

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

[43]  Qingling Zhang,et al.  Stability analysis and observer-based controllers design for T-S fuzzy positive systems , 2018, Neurocomputing.

[44]  Qingling Zhang,et al.  An integral sliding mode control approach to observer-based stabilization of stochastic Itô descriptor systems , 2016, Neurocomputing.

[45]  Karim Dahech,et al.  A sliding mode observer for uncertain nonlinear systems based on multiple models approach , 2017, Int. J. Autom. Comput..

[46]  Yugang Niu,et al.  Observer-based sliding mode control for nonlinear state-delayed systems , 2004, Int. J. Syst. Sci..

[47]  Qingling Zhang,et al.  Novel sliding mode control for multi‐input–multi‐output discrete‐time system with disturbance , 2018 .