## LMI-based fuzzy stability and synchronization of Chen’s system.(English)Zbl 1065.37503

Summary: This Letter presents fuzzy model-based designs for Chen’s chaotic stability and synchronization. The T-S fuzzy model for Chen’s system is exactly derived. Then the asymptotic stability and synchronization are achieved by solving LMI’s design problem. The fuzzy controllers for stability and synchronization with full state variables and single state variable are got respectively by solving LMIs using Matlab. Numerical simulations are shown to verify the results.

### MSC:

 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010)

### Keywords:

asymptotic stability; LMI design problem; fuzzy controllers

Matlab
Full Text:

### References:

 [1] Park, C.-W.; Lee, C.-H.; Park, M., Inform. sci., 147, 245, (2002) [2] Chen, L.; Chen, G.; Lee, Y.-W., Inform. sci., 121, 27, (1999) [3] Lian, K.-Y.; Chiu, C.-S.; Chiang, T.-S.; Liu, P., IEEE trans. fuzzy systems, 9, 4, 539, (2001) [4] Agiza, H.N.; Yassen, M.T., Phys. lett. A, 278, 191, (2001) [5] Guan, Z.-H.; Liao, R.-Q.; Zhou, F.; Wang, H.O., Int. J. bifur. chaos, 12, 5, 1191, (2002) [6] Takagi, T.; Sugeno, M., IEEE trans. systems man cybernet., 15, 1, 116, (1985) [7] Chen, G.; Uet, T., Int. J. bifur. chaos, 9, 7, 1465, (1999) [8] Tanaka, K.; Wang, H.O., Fuzzy control systems design and analysis: A linear matrix inequality approach, (2001), Wiley New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.