非线性奇异摄动系统的反馈镇定  

Feedback Stabilization of Nonlinear Singularly Perturbed Systems

作　　者：孟博[1] 井元伟[1] 刘晓平[1] 

机构地区：[1]东北大学信息科学与工程学院,辽宁沈阳110004

出　　处：《东北大学学报（自然科学版）》2009年第1期5-8,共4页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(60274009);教育部高等学校博士学科点专项科研基金资助项目(20020145007)

摘　　要：针对一类关于快系统是线性的、慢系统可部分输入输出线性化的奇异摄动系统,设计了使整个闭环系统渐近稳定的状态反馈控制器.利用奇异摄动中双时间刻度理论将原系统分解为快慢子系统,其中慢系统具有仿射非线性系统的标准形式,并分别建立了慢系统线性部分和零动态部分及边界层系统的Lyapunov函数;最终通过计算复合Lyapunov函数沿原系统轨线的导数,得到了原系统渐近稳定的充分条件,并给出了估计摄动参数ε上界所满足的定量表达式.仿真实例进一步验证了理论方法的有效性.A state feedback controller is designed for a class of singularly perturbed systems, where the fast systems are linear but the slow ones are partially input/output linearizable. Based on the double time scale theory in singular perturbation, an original system is divided into fast and slow subsystems and the latter are in the standard form of affine nonlinear system. The relevant Lyapunov functions are deduced for the linear part and zero dynamics of slow subsystem and the boundary layer system. As a result, the sufficient conditions for asymptotical stability of the system are given through calculating the derivatives of the composite Lyapunov function along original trajectory, then the upper bound expression of ε singular perturbation parameter is given. Simulation results show the effectiveness and feasibility of the theoretical method proposed.

关 键 词：奇异摄动 双时间刻度 快慢子系统 状态反馈 非线性 

分 类 号：TB114.3[理学—概率论与数理统计] TH122[理学—数学]