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在对已有的混沌系统分析和研究的基础上,将一个二次混沌系统第三个方程关于x的线性项引入到第二个方程中,通过对该系统第二个等式中的线性项x作绝对值运算,提出了一类新的二次非线性系统.采用非线性动力学方法分析了系统参数变化时所经历的稳定、准周期、混沌的过渡过程,模拟电路实验结果与Matlab数值仿真结果相一致.分析发现混沌态时绝对值运算后的系统比原系统的Lyapunov指数更大,并可将原系统的混沌吸引子由两个翼的拓扑结构变为四翼的拓扑结构,从而实现羽翼倍增.针对该混沌特性更强的羽翼倍增混沌系统,基于Takagi-Sugeno(T-S)模糊模型和线性矩阵不等式(LMI),设计出使该羽翼倍增混沌系统渐近稳定的鲁棒模糊控制器.仿真结果证实了所提出定理和设计控制器的有效性.
Based on the analysis and research of the existing chaos system, the linear equation of the third equation of a quadratic chaotic system with respect to x is introduced into the second equation. The linear equation of the second equation x as absolute value operation, a new class of quadratic nonlinear systems is proposed. The nonlinear dynamic method is used to analyze the transition process of stability, quasiperiodicity and chaos experienced by system parameters. The experimental results of simulation circuit and Matlab numerical The results show that the absolute value of the chaotic system is larger than the Lyapunov exponent of the original system and the chaotic attractor of the original system can be changed from the topological structure of the two wings to the topological structure of the four wings Aiming at the double-chaos system with more chaos, a fuzzy controller based on Takagi-Sugeno (TS) fuzzy model and linear matrix inequality (LMI) is designed to make the feathered multiplier chaos system asymptotically stable The simulation results confirm the validity of the proposed theorem and the design of the controller.