The Feasible Control Lyapunov Function of Nonlinear Affine-Control Systems

In order to make the nonlinear affine-control systems become globally asymptotically stable; it is effective to design a kind of feedback controller by means of Lyapunov function. In addition, this way has drawn great attention in recent years. Three things are done in this paper. First, the sufficient and necessary condition about the lower semi-continuousness of feedback control mapping is introduced, which solves the problem on the existence of continuous feedback controller in the nonlinear affine-control systems. Second, the feasible control Lyapunov function is introduced, which restricts the state feedback under permissive scope and makes it more practical. Finally, the feasible control Lyapunov function is replaced by non-strict feasible control Lyapunov function in the nonlinear affine-control systems so that the scope of the control Lyapunov function is expanded.