Stability Analysis for Interval Type-2 Fuzzy Systems by Applying Homogenous Polynomially Membership Functions Dependent Matrices and Switching Technique

In this article, the homogenous polynomially membership functions dependent (HPMFD) matrices are used to study the interval type-2 Takagi–Sugeno fuzzy systems. First, some necessary notations of the HPMFD matrices are introduced. Next, based on these notations, the time derivative of the HPMFD matrices is discussed and a switching method is proposed to ensure that the time derivative of the HPMFD matrices is negative. Then, a HPMFD controller is designed and new stabilization conditions are obtained by using the HPMFD Lyapunov function. In the end, the simulations show that the method in this article is less conservative than the existing ones in the literatures.

[1]  Robert Ivor John,et al.  Geometric Type-1 and Type-2 Fuzzy Logic Systems , 2007, IEEE Transactions on Fuzzy Systems.

[2]  Shaosheng Zhou,et al.  Extended Dissipativity and Control Synthesis of Interval Type-2 Fuzzy Systems via Line-Integral Lyapunov Function , 2020, IEEE Transactions on Fuzzy Systems.

[3]  Ricardo C. L. F. Oliveira,et al.  Parameter-Dependent LMIs in Robust Analysis: Characterization of Homogeneous Polynomially Parameter-Dependent Solutions Via LMI Relaxations , 2007, IEEE Transactions on Automatic Control.

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

[5]  F MontagnerVinícius,et al.  Convergent LMI relaxations for quadratic stabilizability and H∞ control of Takagi-Sugeno fuzzy systems , 2009 .

[6]  Shaocheng Tong,et al.  Adaptive Fuzzy Output Feedback Control for a Class of Nonlinear Systems With Full State Constraints , 2018, IEEE Transactions on Fuzzy Systems.

[7]  Dong Yue,et al.  Observer-Based Fault Estimation for Discrete-Time Nonlinear Systems and Its Application: A Weighted Switching Approach , 2019, IEEE Transactions on Circuits and Systems I: Regular Papers.

[8]  Hak-Keung Lam,et al.  Stability analysis of fuzzy control systems subject to uncertain grades of membership , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[9]  Yung-Sheng Liu,et al.  A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems , 2003, SMC'03 Conference Proceedings. 2003 IEEE International Conference on Systems, Man and Cybernetics. Conference Theme - System Security and Assurance (Cat. No.03CH37483).

[10]  Choon Ki Ahn,et al.  Fuzzy Control and Filtering for Nonlinear Singularly Perturbed Markov Jump Systems , 2020, IEEE Transactions on Cybernetics.

[11]  P. Peres,et al.  Stability of polytopes of matrices via affine parameter-dependent lyapunov functions : Asymptotically exact LMI conditions , 2005 .

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

[13]  Dong Yue,et al.  Control Synthesis of Discrete-Time T–S Fuzzy Systems via a Multi-Instant Homogenous Polynomial Approach , 2016, IEEE Transactions on Cybernetics.

[14]  Hak-Keung Lam,et al.  Further Study on Stabilization for Continuous-Time Takagi-Sugeno Fuzzy Systems With Time Delay. , 2020, IEEE transactions on cybernetics.

[15]  Dong Yue,et al.  Relaxed Real-Time Scheduling Stabilization of Discrete-Time Takagi–Sugeno Fuzzy Systems via An Alterable-Weights-Based Ranking Switching Mechanism , 2018, IEEE Transactions on Fuzzy Systems.

[16]  Ligang Wu,et al.  Optimal Guaranteed Cost Sliding-Mode Control of Interval Type-2 Fuzzy Time-Delay Systems , 2018, IEEE Transactions on Fuzzy Systems.

[17]  Euntai Kim,et al.  New approaches to relaxed quadratic stability condition of fuzzy control systems , 2000, IEEE Trans. Fuzzy Syst..

[18]  Shun-Hung Tsai,et al.  A novel stabilization condition for a class of T-S fuzzy time-delay systems , 2016, Neurocomputing.

[19]  Miguel Bernal,et al.  Towards a global nonquadratic controller design for nonlinear systems via robust differentiators and Takagi-Sugeno models , 2015, 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[20]  Jerry M. Mendel,et al.  Super-Exponential Convergence of the Karnik–Mendel Algorithms for Computing the Centroid of an Interval Type-2 Fuzzy Set , 2007, IEEE Transactions on Fuzzy Systems.

[21]  Yan Yu,et al.  Sampled-Data Output-Feedback Tracking Control for Interval Type-2 Polynomial Fuzzy Systems , 2020, IEEE Transactions on Fuzzy Systems.

[22]  Dan Ye,et al.  Fault-Tolerant Controller Design for General Polynomial-Fuzzy-Model-Based Systems , 2018, IEEE Transactions on Fuzzy Systems.

[23]  Jerry M. Mendel,et al.  Interval Type-2 Fuzzy Logic Systems Made Simple , 2006, IEEE Transactions on Fuzzy Systems.

[24]  Minrui Fei,et al.  Local stability conditions for T-S fuzzy time-delay systems using a homogeneous polynomial approach , 2020, Fuzzy Sets Syst..

[25]  Hak-Keung Lam,et al.  Stability Analysis of Interval Type-2 Fuzzy-Model-Based Control Systems , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[26]  Dong Yue,et al.  Relaxed Control Design of Discrete-Time Takagi–Sugeno Fuzzy Systems: An Event-Triggered Real-Time Scheduling Approach , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[27]  Xiangpeng Xie,et al.  Sliding-Mode Control of Fuzzy Singularly Perturbed Descriptor Systems , 2021, IEEE Transactions on Fuzzy Systems.

[28]  Ligang Wu,et al.  State and Output Feedback Control of Interval Type-2 Fuzzy Systems With Mismatched Membership Functions , 2015, IEEE Transactions on Fuzzy Systems.

[29]  Dan Ye,et al.  Asynchronous Event-Triggered Control for Networked Interval Type-2 Fuzzy Systems Against DoS Attacks , 2021, IEEE Transactions on Fuzzy Systems.

[30]  Changchun Hua,et al.  Adaptive Fuzzy Prescribed Performance Control for Nonlinear Switched Time-Delay Systems With Unmodeled Dynamics , 2018, IEEE Transactions on Fuzzy Systems.

[31]  Hak-Keung Lam,et al.  Further Study on Observer Design for Continuous-Time Takagi–Sugeno Fuzzy Model With Unknown Premise Variables via Average Dwell Time , 2020, IEEE Transactions on Cybernetics.

[32]  Hak-Keung Lam,et al.  A review on stability analysis of continuous-time fuzzy-model-based control systems: From membership-function-independent to membership-function-dependent analysis , 2018, Eng. Appl. Artif. Intell..

[33]  Ligang Wu,et al.  Analysis and Synthesis for Interval Type-2 Fuzzy-Model-Based Systems , 2016 .

[34]  Baocang Ding,et al.  Homogeneous Polynomially Nonquadratic Stabilization of Discrete-Time Takagi–Sugeno Systems via Nonparallel Distributed Compensation Law , 2010, IEEE Transactions on Fuzzy Systems.

[35]  Renquan Lu,et al.  Finite-Horizon $H_{\infty}$ State Estimation for Periodic Neural Networks Over Fading Channels , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[36]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[37]  Hak-Keung Lam,et al.  A Polynomial Membership Function Approach for Stability Analysis of Fuzzy Systems , 2020, IEEE Transactions on Fuzzy Systems.

[38]  Antonio Sala,et al.  Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Polya's theorem , 2007, Fuzzy Sets Syst..

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

[40]  Hak-Keung Lam,et al.  Analysis and Design of Interval Type-2 Polynomial-Fuzzy-Model-Based Networked Tracking Control Systems , 2021, IEEE Transactions on Fuzzy Systems.

[41]  Xiaodong Liu,et al.  Approaches to quadratic stability conditions and H∞ control designs for T-S fuzzy systems , 2003, IEEE Trans. Fuzzy Syst..

[42]  Xiaodong Liu,et al.  Stability analysis for discrete‐time fuzzy system by utilizing homogeneous polynomial matrix function , 2009 .