基于拟单边Lipschitz条件的一类非线性系统降维观测器设计

Reduced-order observer design for a class of nonlinear systems based on a quasi-one-sided Lipschitz condition

为了研究一类非线性系统降维观测器设计问题,引入拟单边、弱拟单边Lipschitz条件,采用线性矩阵不等式方法给出了该类系统降维观测器渐近稳定的判据.借助(弱)拟单边Lipschitz条件,研究了系统非线性项对降维观测误差渐近收敛性的贡献,得到了比现有的方法减小保守性的判据.证明了在系统的参数不可检测性时,所给出的判据仍然有效.最后,给出仿真算例并验证了所得方法的正确性.

In order to study the problem of reduced-order observer design for a class of nonlinear systems,the quasi-one-sided and weak-quasi-one-sided Lipschitz conditions were introduced.Criteria for the existence of reduced-order observers of the class of nonlinear systems were presented the linear matrix inequality method.Based on the（weak-） quasi-one-sided Lipschitz condition,the contribution of the nonlinearity on asymptotic convergence of the observer error was explored.The proposed criteria were less conservative than those in previous literature.Furthermore,it was proven that the present criteria are available even if the system parameters are not detectable.Two numerical examples were given to illustrate effects of the proposed approach.