Observer-based control for uncertain T–S fuzzy systems with process disturbances and time-delays

ABSTRACT This paper concerns the observer-based robust control for uncertain Takagi–Sugeno(T–S) fuzzy systems with disturbances and time delays. An observer is firstly employed to estimate the system state, afterwards, a memorise feedback control law is furthermore proposed. Since the observer state can not be directly influenced by the system uncertainties and disturbances, the proposed control law brings merit on improving system robustness. A mode-dependent Lyapunov-Krasovskii functional (LKF) is designed. By aid of a linear decoupling method, the original nonlinear pair of the observer and the controller gains can be feasibly decoupled. By this method, the co-design method of the observer and controller is conveniently presented. In presence of the time-varying delays, process disturbances and the system uncertainties, the asymptotical stability of the closed-loop system can be guaranteed. Numerical example is given the validate effectiveness of the proposed method.

[1]  Jin-Hoon Kim,et al.  Further improvement of Jensen inequality and application to stability of time-delayed systems , 2016, Autom..

[2]  Ju H. Park,et al.  Stability of time-delay systems via Wirtinger-based double integral inequality , 2015, Autom..

[3]  Sangchul Won,et al.  A new fuzzy Lyapunov function approach for a Takagi-Sugeno fuzzy control system design , 2006, Fuzzy Sets Syst..

[4]  Ning Li,et al.  Robust H∞ control of uncertain linear system with interval time-varying delays by using Wirtinger inequality , 2018, Appl. Math. Comput..

[5]  Bing Chen,et al.  A novel Lyapunov-Krasovskii functional approach to stability and stabilization for T-S fuzzy systems with time delay , 2018, Neurocomputing.

[6]  Faris Alzahrani,et al.  Observer-based memory consensus for nonlinear multi-agent systems with output quantization and Markov switching topologies , 2020 .

[7]  Min Wu,et al.  An extended reciprocally convex matrix inequality for stability analysis of systems with time-varying delay , 2017, Autom..

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

[9]  Hamid Reza Karimi,et al.  Observer-based robust H∞ vibration control of a half-car active suspension system: A finite-time approach , 2020 .

[10]  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.

[11]  Arash Farnam,et al.  Improved linear matrix inequality approach to stability analysis of linear systems with interval time-varying delays , 2016, J. Comput. Appl. Math..

[12]  B. G. Grebenshchikov,et al.  Stabilization of some systems with constant delay , 2018 .

[13]  Yong He,et al.  Further robust stability analysis for uncertain Takagi-Sugeno fuzzy systems with time-varying delay via relaxed integral inequality , 2017, Inf. Sci..

[14]  P. Khargonekar,et al.  Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory , 1990 .

[15]  Minrui Fei,et al.  Improved H∞ consensus of multi-agent systems under network constraints within multiple disturbances , 2016, Int. J. Control.

[16]  Yong-Ki Ma,et al.  Observer-Based $H_\infty$ Repetitive Control for Fractional-Order Interval Type-2 TS Fuzzy Systems , 2018, IEEE Access.

[17]  Bing Chen,et al.  New stability and stabilization conditions for T-S fuzzy systems with time delay , 2015, Fuzzy Sets Syst..

[18]  Lin Chen,et al.  Stability and stabilization of T-S fuzzy systems with time delay via Wirtinger-based double integral inequality , 2018, Neurocomputing.

[19]  Yanliang Cui,et al.  H2/H∞ filtering for networked systems with data transmission time-varying delay, data packet dropout and sequence disorder , 2017, J. Frankl. Inst..

[20]  Sever Silvestru Dragomir.  A new refinement of Jensen's inequality in linear spaces with applications , 2010, Math. Comput. Model..

[21]  Sang-Moon Lee,et al.  Enhanced stability criteria of neural networks with time-varying delays via a generalized free-weighting matrix integral inequality , 2018, J. Frankl. Inst..

[22]  Peng Shi,et al.  Functional observer based controller for stabilizing Takagi-Sugeno fuzzy systems with time-delays , 2018, J. Frankl. Inst..

[23]  Frédéric Gouaisbaut,et al.  On the Use of the Wirtinger Inequalities for Time-Delay Systems , 2012, TDS.

[24]  Yu Fu,et al.  Fuzzy Logic Aided Fault-Tolerant Control Applied to Transport Aircraft Subject to Actuator Stuck Failures , 2018, IEEE Transactions on Fuzzy Systems.

[25]  Yongduan Song,et al.  A Novel Control Design on Discrete-Time Takagi–Sugeno Fuzzy Systems With Time-Varying Delays , 2013, IEEE Transactions on Fuzzy Systems.

[26]  Yanliang Cui,et al.  Chattering‐free adaptive sliding mode control for continuous‐time systems with time‐varying delay and process disturbance , 2019, International Journal of Robust and Nonlinear Control.

[27]  Yong He,et al.  Delay-dependent criteria for robust stability of time-varying delay systems , 2004, Autom..

[28]  Hieu Minh Trinh,et al.  A common functional observer scheme for three systems with unknown inputs , 2016, J. Frankl. Inst..

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

[30]  Yanliang Cui,et al.  Robust H∞ persistent dwell time control for switched discrete-time T-S fuzzy systems with uncertainty and time-varying delay , 2019, J. Frankl. Inst..

[31]  Minrui Fei,et al.  Design of a robust observer‐based memoryless H∞ control for internet congestion , 2016 .

[32]  D. Ho,et al.  Robust stabilization for a class of discrete-time non-linear systems via output feedback: The unified LMI approach , 2003 .

[33]  Yanliang Cui,et al.  Active vibration control for seismic excited building structures under actuator saturation, measurement stochastic noise and quantisation , 2018 .

[34]  Hamid Reza Karimi,et al.  Observer-based finite-time fuzzy H∞ control for discrete-time systems with stochastic jumps and time-delays , 2014, Signal Process..

[35]  PooGyeon Park,et al.  Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems , 2015, J. Frankl. Inst..

[36]  Jianbin Qiu,et al.  Observer-Based Piecewise Affine Output Feedback Controller Synthesis of Continuous-Time T–S Fuzzy Affine Dynamic Systems Using Quantized Measurements , 2012, IEEE Transactions on Fuzzy Systems.