Abstract
In the disturbance decoupling problem (DDP) of the linear system (A, B, C), the A-invariant subspace and the (A, B)-invariant subspace are proved to play a key role. The purpose of this paper is to extend the study of the DDP to nonlinear control systems.
It must be noted that the problems are stated on the tangent bundle over the state space. The state space and the tangent bundle over it can be identified in the analysis of linear systems, but they must be distinguished in the case of nonlinear systems. So it is needed to establish the corresponding concepts in the state space to extend the A-invariance and the (A, B)-invariance to nonlinear systems. From such a point of view, the invariant structure and the structure which can be modified invariant by nonlinear state feedback are introduced as the state space representations of the A-invariant subspace and the (A, B)-invariant subspace.
The main result obtained here, is the algebraic necessary and sufficient condition for the DDP of the nonlinear control systems.
