On stability of linear switching systems

This dissertation is about switching systems. In chapter 1, the background of stability of linear switching systems is introduced; In chapter 2, some su cient conditions in terms of relation between eigenvalues and eigenvectors of switching matrices are given for asymptotic stability under arbitrary switching scheme, and are followed by several examples for n = 2; In chapter 3, some results about stability after state feedback are discussed, and a necessary and su cient condition is given for the existence of a common quadratic Lyapunov function of the closed-loop system; In chapter 4, it is shown that asymptotic stability depends on the average switching rate; some methods to obtain maximal switching rate are given, especially when switching matrices are semi-simple.