线性系统能观性的鲁棒性

Robustness of observability of linear systems

为说明线性化方法在非线性系统能观性分析中的合理性,在状态方程和输出方程存在非线性摄动项的情况下,对线性系统能观性的鲁棒性进行了研究。首先对零输入线性定常系统,证明了若摄动项在平衡点附近具有高阶无穷小的性质,则线性系统的能观性蕴含摄动系统在平衡点附近的能观性,然后将该结论在一定的假设条件下推广至零输入线性时变系统。最后,作为结论的进一步说明和应用,给出了两个数值算例。

The robustness of observability is studied for linear systems under nonlinear perturbations in the state dynamics and the output channel.For time-invariant linear systems,it is shown that the observability will be locally preserved if the perturbations have the property of higher order infinitesimal.Further,this result is extended to time-varying linear systems,which demonstrates the validity of linearization for observability analysis of nonlinear systems.Two numerical examples are given to illustrate the presented result.