首先基于系数矩阵的一致对称正定性建立了二阶线性时变系统稳定性的一个判据.该判据简单、明了,是作者早期给出的关于定常二节线性系统稳定性判据的直接推广. 基于这一判据,文章进一步给出了具有参数不确定性的二阶线性时变系统的鲁棒稳定性.所得结果对于处理确定性二阶线性时变系统镇定问题和不确定性二阶线性时变系统的鲁棒镇定问题提供了便捷而有效的工具. 最后,文章将提出的方法应用到某卫星姿态系统的控制中.

In this paper, a simple criterion for stability of second-order time-varying linear systems is firstly proposed in terms of the uniformly symmetric positivity of the coefficient matrices, which is a generalization of a former result for constant second-order linear systems, in a very neat and simple form. Secondly, based on this result, the robust stability of second-order time-varying linear systems with coefficient uncertainties is also provided. These results provide convenient and efficient tools for stabilization and robust stabilization of deterministic and uncertain second-order time-varying linear systems. Finally, an application of the proposed results to a satellite attitude system is presented.