关联系统稳定性分析的线性比较方程计算
Computation of Linear Comparison Equations for Stability Analysis of Interconnected Systems
摘要：
平方和（SOS）方法已被证明是非常有用的计算多项式李雅普诺夫函数的系统，合理的小尺寸。然而，对于大规模的系统，有必要使用一个可扩展的替代使用向量李雅普诺夫函数。早期的工作表明，在一定条件下，关联系统的稳定性可以通过适当的比较方程来研究。然而，找到这样的比较方程可能是不平凡的。在这项工作中，我们提出了一个SOS为基础的系统程序直接计算比较方程的关联系统多项式动力学。通过一个相互作用的Van der Pol系统的例子，我们说明了这是如何促进稳定性分析的可扩展性和并行方法。
英文摘要：
Sum-of-squares (SOS) methods have been shown to be very useful in computing polynomial Lyapunov functions for systems of reasonably small size. However for large scale systems it is necessary to use a scalable alternative using vector Lyapunov functions. Earlier works have shown that under certain conditions the stability of an interconnected system can be studied through suitable comparison equations. However finding such comparison equations can be non-trivial. In this work we propose an SOS based systematic procedure to directly compute the comparison equations for interconnected system with polynomial dynamics. With an example of interacting Van der Pol systems, we illustrate how this facilitates a scalable and parallel approach to stability analysis.
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