Lipschitz非线性系统的鲁棒干扰抑制能力

研究了Lipschitz常数与干扰抑制度之间的关系·通过对Lipschitz非线性系统设计具有干扰抑制的状态观测器,给出了该观测器渐近稳定的充分条件·在此基础上,针对外界干扰为能量有界的情况,得到了Lipschitz常数与给定的H∞干扰抑制指标之间定量的显示表达关系,并将其转化为对Riccati不等式的分析·结果表明,较大的Lipschitz常数一般对应较大的干扰抑制度,从而对Lipschitz非线性系统干扰抑制能力有了定量认识·

Robust Capability of Disturbance Rejection for Nonlinear Systems Satisfying Lipschitz Condition

The relation between Lipschitz constant and index of disturbance rejection has been studied quantitatively. By designing a full-order state observer with disturbance rejection for the nonlinear systems satisfying Lipschitz condition, a sufficient condition of the stability of the observer is given by using H∞ technique. In case the energy of external disturbance is finite, an explicit expression between Lipschitz constant and index of H∞ disturbance rejection is obtained by transforming the expression to Riccati inequality. A conclusion is thus drawn that generally the greater the Lipschitz constant is, the higher the index of disturbance rejection will be, and vice versa. In view of the index of disturbance rejection, the nonlinear system satisfying Lipschitz condition to a certain degree is therefore considered quantitatively as that it hasn't a robust but weak capability of disturbance rejection.