Practical Stabilization of Nonlinear Control Systems

Abstract

Motivated by the observation that if det(B)≠0 in a linear system (A, B), the controller design problem is trivial in some sense, the concept of full-controlled system will be introduced. It is shown every strongly attainable nonlinear control system can be decomposed to a series of full-controlled subsystems by introducing the virtual input variables. The decomposition is called the virtual decomposition. A nonlinear full-controlled subsystems do not have so good properties as linear ones. To discuss the stabilization problem of the virtually decomposed system, the concept of the practical stabilization has been introduced. A system is called practically stabilizable if the trajectory of the system has been confined in the arbitrary small neighborhood of the equlibrium point by the state feedback. A full controlled system is called completely decomposable if it admits the decomposition to scalar subsystems which are linear in input. It is shown that the completely decomposable full-controlled systems are practically stabilizable. Finally, a controller design method will be proposed for the virtually decomposed nonlinear systems.