C0-stabilizablity of nonlinear control-affine systems
非线性仿射控制系统的C0镇定性

In order to eliminate the difficulty in the design of Lyapunov function proposed by Sontag,the C~0-stabilizab- lity of nonlinear affine control systems is studied in this paper.Firstly,the accumulation point condition is briefly introduced in order to ensure the continuity of the Sontag's formula.Secondly,the accumulation point condition is also proved to be necessary for the continuity of Sontag's formula.Thirdly,the strict control Lyapunov function is replaced by non-strict control Lyapunov function in the nonlinear affine control systems.Motivated by LaSalle theorem,the system with non- strict Lyapunov function which is said to satisfy the accumulation point condition is proved to be C~0-stabilizable,the optional range of Lyapunov function is thus extended.Finally,an example of frictional spring system is given to validate this theory.