论文标题
一种计算开关线性系统稳定余量的数值方法
A Numerical Method to Compute Stability Margins of Switching Linear Systems
论文作者
论文摘要
传统上，通过二次lyapunov函数计算线性时变（LTV）和切换线性系统的稳定性边缘，这些功能证明了正在研究的系统的稳定性。在这项工作中，我们展示了更一般的均质多项式Lyapunov函数如何使用降低的保守主义来计算稳定边缘，并且我们展示了这些Lyapunov的功能如何有助于寻找边缘稳定的LTV系统的周期性轨迹。我们的工作基于最近的观察，即某些LTV系统寻找同质多项式Lyapunov函数很容易编码，因为寻找相关LTV系统的二次lyapunov函数，而我们的主要贡献是一种直观的算法，用于在系统的上限和下限系统的稳定性元素上产生上限和下限。我们还展示了如何生成最接近周期性轨道的LTV系统的最坏情况开关方案。提供了三个数字示例，以帮助读者并演示工作的理论贡献。
Stability margins for linear time-varying (LTV) and switched-linear systems are traditionally computed via quadratic Lyapunov functions, and these functions certify the stability of the system under study. In this work, we show how the more general class of homogeneous polynomial Lyapunov functions is used to compute stability margins with reduced conservatism, and we show how these Lyapunov functions aid in the search for periodic trajectories for marginally stable LTV systems. Our work is premised on the recent observation that the search for a homogeneous polynomial Lyapunov function for some LTV systems is easily encoded as the search for a quadratic Lyapunov function for a related LTV system, and our main contribution is an intuitive algorithm for generating upper and lower bounds on the system's stability margin. We show also how the worst-case switching scheme - which draws an LTV system closest to a periodic orbit - is generated. Three numerical examples are provided to aid the reader and demonstrate the theoretical contributions of the work.
