Chaotification for switched linear systems with controllers  

作　　者：解玲丽 

机构地区：[1]Department of Mathematics,Sun Yat-sen University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2013年第9期1167-1174,共8页应用数学和力学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.11071262,11101440,and 61263011)

摘　　要：This paper shows that two or more switched linear systems can generate chaotic dynamical behaviors by an appropriate switching rule as they at least consist of a controllable system and an unstable system with the expanding property. According to the results in the reference （Xie, L. L., Zhou, Y., and Zhao, Y. Criterion of chaos for switched linear systems with antrollers. International Journal of Bifurcation and Chaos, 20（12）, 4105-4109 （2010））, a nonlinear feedback gain is needed to generate chaotic dy- namics. A linear feedback control is usually used to approximate the nonlinear one for simulation. In order to obtain the exact control, as a main result of this paper, the con- troller is constructed by Russell＇s result, and a block diagram is included to interpret the realization of the controller. Numerical simulations are given to illustrate the generated chaotic dynamical behavior of the switched linear systems with some parameters and show the effects of the constructed controller.This paper shows that two or more switched linear systems can generate chaotic dynamical behaviors by an appropriate switching rule as they at least consist of a controllable system and an unstable system with the expanding property. According to the results in the reference （Xie, L. L., Zhou, Y., and Zhao, Y. Criterion of chaos for switched linear systems with antrollers. International Journal of Bifurcation and Chaos, 20（12）, 4105-4109 （2010））, a nonlinear feedback gain is needed to generate chaotic dy- namics. A linear feedback control is usually used to approximate the nonlinear one for simulation. In order to obtain the exact control, as a main result of this paper, the con- troller is constructed by Russell＇s result, and a block diagram is included to interpret the realization of the controller. Numerical simulations are given to illustrate the generated chaotic dynamical behavior of the switched linear systems with some parameters and show the effects of the constructed controller.

关 键 词：CHAOTIFICATION switched linear system construction of controller 

分 类 号：O231.5[理学—运筹学与控制论]