【作者】 倪郁东； 费树岷； 沈吟东；

【Author】 NI Yu-dong~(1,2),FEI Shu-min~2,SHEN Yin-dong~3 1.Hefei University of Technology,Hefei,230009,China 2.Key Laboratory of Measurement and Control of CSE,Ministry of Education School of Automation,Southeast University,Nanjing,210096,China 3.Huazhong University of Science and Technology,Wuhan,430074,China

【机构】 合肥工业大学数学系； 复杂工程系统测量与控制教育部重点实验室/东南大学自动化学院； 华中科技大学控制科学与工程系；

【摘要】 考察二维仿射控制系统在具有一对共轭纯虚数特征值的临界状态下的局部光滑镇定性。应用非奇异线性状态变换和时问尺度变换,将系统转化成标准形式。运用扩展正则判别函数法和形式级数法的思想,构造多组线性方程组,给出确定光滑控制律和闭环系统李雅普诺夫函数的一种方法,从而得到该系统局部光滑镇定的充分条件。示例说明该方法是有效的。更多还原

【Abstract】 This paper studies the local smooth stabilizability of the 2-dimension nonlinear control system,which possesses a pair of conjugated imaginary eigenvalues.The system is firstly transformed to a standard formula by the non-singularity linear coordinate transformation and the time scale transformation as well.Next,the approaches for determining smooth control law and Lyapunov function of the closed loop system are provided by the construction of several sets of linear equations based on the expanded canonical discriminant function and the formal progression method.Finally,a sufficient condition of the local smooth stabilizability to the system is obtained,the validity of which is shown by an example.更多还原