Generating Li Yorke chaos in a stable continuous-time T S fuzzy model via time-delay feedback control

This paper investigates the chaotification problem of a stable continuous-time T–S fuzzy system. A simple nonlinear state time-delay feedback controller is designed by parallel distributed compensation technique. Then, the asymptotically approximate relationship between the controlled continuous-time T–S fuzzy system with time-delay and a discrete-time T–S fuzzy system is established. Based on the discrete-time T–S fuzzy system, it proves that the chaos in the discrete-time T–S fuzzy system satisfies the Li–Yorke definition by choosing appropriate controller parameters via the revised Marotto theorem. Finally, the effectiveness of the proposed chaotic anticontrol method is verified by a practical example.

[1]  Ding Liu,et al.  Nonlinear feedback control of chaos in permanent magnet synchronous motor , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[2]  Xingyuan Wang,et al.  A hyperchaos generated from Lorenz system , 2008 .

[3]  Tatsuo Narikiyo,et al.  Abrasive Machining under Wet Condition and Constant Pressure using Chaotic Rotation. , 1998 .

[4]  Guanrong Chen,et al.  Single State-Feedback Chaotification of Discrete Dynamical Systems , 2004, Int. J. Bifurc. Chaos.

[5]  M. F. Edwards,et al.  Mixing in the process industries , 1985 .

[6]  Zhao Yan,et al.  A unified approach to fuzzy modelling and robust synchronization of different hyperchaotic systems , 2008 .

[7]  谢剑英,et al.  Chaotifying a stable linear controllable system by single input state feedback , 2007 .

[8]  Jin Bae Park,et al.  Anticontrol of Chaos for a Continuous-Time Takagi-sugeno Fuzzy System via Local Time-Delay Feedback , 2005, Int. J. Bifurc. Chaos.

[9]  Xing-yuan Wang,et al.  Projective synchronization of fractional order chaotic system based on linear separation , 2008 .

[10]  Lu Qi-Shao,et al.  Coherence resonance and synchronization of Hindmarsh Rose neurons with noise , 2005 .

[11]  Guan Zhi-hong,et al.  Chaotification for a class of nonlinear systems , 2009 .

[12]  朱杰,et al.  Decentralized state-feedback chaotification method of discrete Takagi Sugeno fuzzy systems , 2005 .

[13]  Fu Jie,et al.  A practical approach to robust impulsive lag synchronization between different chaotic systems , 2008 .

[14]  Zhang Huaguang,et al.  Exponential synchronization of stochastic impulsive perturbed chaotic Lur'e systems with time-varying delay and parametric uncertainty , 2008 .

[15]  Wang Xingyuan,et al.  Observer-based adaptive fuzzy synchronization for hyperchaotic systems. , 2008, Chaos.

[16]  Zhao Yan,et al.  Anticontrol of chaos for discrete-time fuzzy hyperbolic model with uncertain parameters , 2008 .

[17]  Huaguang Zhang,et al.  Chaotifying Fuzzy Hyperbolic Model Using impulsive and Nonlinear Feedback Control Approaches , 2005, Int. J. Bifurc. Chaos.

[18]  卢俊国.  Chaotifying a stable Takagi–Sugeno fuzzy system by a sawtooth nonlinearity , 2005 .

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

[20]  F. R. Marotto.  On redefining a snap-back repeller , 2005 .

[21]  Y. P. Zhang,et al.  Study of runaway electron behaviour during electron cyclotron resonance heating in the HL-2A Tokamak , 2009 .