Constructing Common Quadratic Lyapunov Functions for a Class of Stable Matrices

Narendra 和 Balakrishnan 建议了一个方法构造普通二次的 Lyapunov 功能(CQLF )[1 ] ，稳定的矩阵的 whena 集合是可交换的。这份报纸的目的是概括方法到非可交换、非可解决的大小写。一个修改构造算法被建议，某些条件被提供向是的矩阵保证结果 CQLF。下次，讨论的问题是一个稳定的矩阵什么时候能与 CQLF 被加到一套矩阵为扩大集合构造新 CQLF。

Narendra and Balakrishnan proposed a way to construct a common quadratic Lyapunov function （CQLF）, when a set of stable matrices axe commutative. The purpose of this paper is to generalize the method to non-commutative and non-solvable case. A modified constructing algorithm is proposed and certain conditions axe provided to assure the resulting matrix being a CQLF. Next, the problem discussed is when a stable matrix can be added to a set of matrices with CQLF to construct a new CQLF for the enlarged set.