Almost Global Stability Of Several Systems

This paper studys almost global stability for several systems.First through the ac-knowledge of matrix theory and measure theory,a sufficient and necessary condition is proved for almost global stability of linear time-invariant system,that is A is Hurwitz ma-trix and use the way of linearization to study almost local stability of the nonlinear system. Second, We consider general switching systems, under an additional assumption, We con-struct a switching rule depending on state space which can ensure the system's almost global stability in a very general sense. At last,this paper studys unstability for nonlinear systems, use a maximum function and Grawall inequality to prove existence of a scalar function satisfying certain inequality, it follows that almost all trajectories of the system converge to infinity.